Semantic Graph — Visual Examination Report

{
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    {
      "id": "P",
      "type": "scalar",
      "latex": "P",
      "subexpr": "P",
      "chartScript": {
        "script": "P",
        "variables": [
          "P"
        ]
      }
    },
    {
      "id": "Q",
      "type": "scalar",
      "latex": "Q",
      "subexpr": "Q",
      "chartScript": {
        "script": "Q",
        "variables": [
          "Q"
        ]
      }
    },
    {
      "id": "__implies_1",
      "type": "operator",
      "label": "implies",
      "emoji": "⇒",
      "op": "implies",
      "subexpr": "P \\implies Q",
      "chartScript": {
        "script": "P*Q*implies",
        "variables": [
          "P",
          "Q",
          "implies"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "P",
      "to": "__implies_1",
      "role": "lhs"
    },
    {
      "from": "Q",
      "to": "__implies_1",
      "role": "rhs"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
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  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  P["$P$"]:::scalar
  Q["$Q$"]:::scalar
  __implies_1(("$\Rightarrow$")):::operator
  P -->|lhs| __implies_1
  Q -->|rhs| __implies_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "P",
      "type": "scalar",
      "latex": "P",
      "subexpr": "P",
      "chartScript": {
        "script": "P",
        "variables": [
          "P"
        ]
      }
    },
    {
      "id": "Q",
      "type": "scalar",
      "latex": "Q",
      "subexpr": "Q",
      "chartScript": {
        "script": "Q",
        "variables": [
          "Q"
        ]
      }
    },
    {
      "id": "__iff_1",
      "type": "operator",
      "label": "if and only if",
      "emoji": "⇔",
      "op": "iff",
      "subexpr": "P \\iff Q",
      "chartScript": {
        "script": "P*Q*iff",
        "variables": [
          "P",
          "Q",
          "iff"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "P",
      "to": "__iff_1"
    },
    {
      "from": "Q",
      "to": "__iff_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
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  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
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  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  P["$P$"]:::scalar
  Q["$Q$"]:::scalar
  __iff_1(("$\Leftrightarrow$")):::operator
  P --> __iff_1
  Q --> __iff_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "R",
      "type": "scalar",
      "latex": "\\mathbb{R}",
      "subexpr": "{R}",
      "chartScript": {
        "script": "R",
        "variables": [
          "R"
        ]
      }
    },
    {
      "id": "__element_of_1",
      "type": "relation",
      "label": "element of",
      "emoji": "∈",
      "op": "element_of",
      "subexpr": "x \\in \\mathbb{R}",
      "chartScript": {
        "script": "R*in*mathbb*x",
        "variables": [
          "R",
          "in",
          "mathbb",
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__element_of_1",
      "role": "lhs"
    },
    {
      "from": "R",
      "to": "__element_of_1",
      "role": "rhs"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  x["$x$"]:::scalar
  R["$\mathbb{R}$"]:::scalar
  __element_of_1{"∈"}:::relation
  x -->|lhs| __element_of_1
  R -->|rhs| __element_of_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "Z",
      "type": "scalar",
      "latex": "\\mathbb{Z}",
      "subexpr": "{Z}",
      "chartScript": {
        "script": "Z",
        "variables": [
          "Z"
        ]
      }
    },
    {
      "id": "__not_element_of_1",
      "type": "relation",
      "label": "not element of",
      "emoji": "∉",
      "op": "not_element_of",
      "subexpr": "x \\notin \\mathbb{Z}",
      "chartScript": {
        "script": "Z*mathbb*notin*x",
        "variables": [
          "Z",
          "mathbb",
          "notin",
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__not_element_of_1",
      "role": "lhs"
    },
    {
      "from": "Z",
      "to": "__not_element_of_1",
      "role": "rhs"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  x["$x$"]:::scalar
  Z["$\mathbb{Z}$"]:::scalar
  __not_element_of_1{"∉"}:::relation
  x -->|lhs| __not_element_of_1
  Z -->|rhs| __not_element_of_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__multiply_1",
      "type": "operator",
      "op": "multiply",
      "subexpr": "A \\subseteq B",
      "chartScript": {
        "script": "A*B*subseteq",
        "variables": [
          "A",
          "B",
          "subseteq"
        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "A",
      "subexpr": "A",
      "chartScript": {
        "script": "A",
        "variables": [
          "A"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\subseteq B",
      "chartScript": {
        "script": "B*subseteq",
        "variables": [
          "B",
          "subseteq"
        ]
      }
    },
    {
      "id": "subseteq",
      "type": "scalar",
      "latex": "\\subseteq",
      "subexpr": "\\subseteq",
      "chartScript": {
        "script": "subseteq",
        "variables": [
          "subseteq"
        ]
      }
    },
    {
      "id": "B",
      "type": "scalar",
      "latex": "B",
      "subexpr": "B",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "A",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "subseteq",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "B",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __multiply_1(("$\times$")):::operator
  A["$A$"]:::scalar
  __multiply_2(("$\times$")):::operator
  subseteq["$\subseteq$"]:::scalar
  B["$B$"]:::scalar
  A --> __multiply_1
  subseteq --> __multiply_2
  B --> __multiply_2
  __multiply_2 --> __multiply_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "A \\cup B = B \\cup A",
      "chartScript": {
        "script": "True",
        "variables": []
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "A",
      "subexpr": "A",
      "chartScript": {
        "script": "A",
        "variables": [
          "A"
        ]
      }
    },
    {
      "id": "B",
      "type": "scalar",
      "latex": "B",
      "subexpr": "B",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    },
    {
      "id": "__union_2",
      "type": "operator",
      "emoji": "∪",
      "op": "union",
      "subexpr": "A \\cup B",
      "chartScript": {
        "script": "A*B*cup",
        "variables": [
          "A",
          "B",
          "cup"
        ]
      }
    },
    {
      "id": "__union_3",
      "type": "operator",
      "emoji": "∪",
      "op": "union",
      "subexpr": "B \\cup A",
      "chartScript": {
        "script": "A*B*cup",
        "variables": [
          "A",
          "B",
          "cup"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "A",
      "to": "__union_2"
    },
    {
      "from": "B",
      "to": "__union_2"
    },
    {
      "from": "__union_2",
      "to": "__equals_1"
    },
    {
      "from": "B",
      "to": "__union_3"
    },
    {
      "from": "A",
      "to": "__union_3"
    },
    {
      "from": "__union_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  A["$A$"]:::scalar
  B["$B$"]:::scalar
  __union_2(("$\cup$")):::operator
  __union_3(("$\cup$")):::operator
  A --> __union_2
  B --> __union_2
  __union_2 --> __equals_1
  B --> __union_3
  A --> __union_3
  __union_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__multiply_1",
      "type": "operator",
      "op": "multiply",
      "subexpr": "A \\cap B \\subseteq  A",
      "chartScript": {
        "script": "pow(A, 2)*B*cap*subseteq",
        "variables": [
          "A",
          "B",
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        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "A",
      "subexpr": "A",
      "chartScript": {
        "script": "A",
        "variables": [
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        ]
      }
    },
    {
      "id": "B",
      "type": "scalar",
      "latex": "B",
      "subexpr": "B",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    },
    {
      "id": "__intersection_2",
      "type": "operator",
      "emoji": "∩",
      "op": "intersection",
      "subexpr": "A \\cap B",
      "chartScript": {
        "script": "A*B*cap",
        "variables": [
          "A",
          "B",
          "cap"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "A \\subseteq",
      "chartScript": {
        "script": "A*subseteq",
        "variables": [
          "A",
          "subseteq"
        ]
      }
    },
    {
      "id": "subseteq",
      "type": "scalar",
      "latex": "\\subseteq",
      "subexpr": "\\subseteq",
      "chartScript": {
        "script": "subseteq",
        "variables": [
          "subseteq"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "A",
      "to": "__intersection_2"
    },
    {
      "from": "B",
      "to": "__intersection_2"
    },
    {
      "from": "__intersection_2",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "subseteq",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "A",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
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  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __multiply_1(("$\times$")):::operator
  A["$A$"]:::scalar
  B["$B$"]:::scalar
  __intersection_2(("$\cap$")):::operator
  __multiply_3(("$\times$")):::operator
  subseteq["$\subseteq$"]:::scalar
  A --> __intersection_2
  B --> __intersection_2
  __intersection_2 --> __multiply_1
  subseteq --> __multiply_3
  A --> __multiply_3
  __multiply_3 --> __multiply_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "(A \\cup B)^c  = A^{c} \\cap B^{c}",
      "chartScript": {
        "script": "-pow(A, c)*pow(B, c)*cap + pow(A*B*cup, c)",
        "variables": [
          "A",
          "B",
          "c",
          "cap",
          "cup"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "op": "power",
      "subexpr": "(A \\cup B)^{c}",
      "chartScript": {
        "script": "pow(A*B*cup, c)",
        "variables": [
          "A",
          "B",
          "c",
          "cup"
        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
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      "subexpr": "A",
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      "chartScript": {
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      }
    },
    {
      "id": "__union_3",
      "type": "operator",
      "emoji": "∪",
      "op": "union",
      "subexpr": "A \\cup B",
      "chartScript": {
        "script": "A*B*cup",
        "variables": [
          "A",
          "B",
          "cup"
        ]
      }
    },
    {
      "id": "c",
      "type": "scalar",
      "latex": "c",
      "subexpr": "c",
      "chartScript": {
        "script": "c",
        "variables": [
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      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "subexpr": "A^{c}",
      "chartScript": {
        "script": "pow(A, c)",
        "variables": [
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          "c"
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      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "subexpr": "B^{c}",
      "chartScript": {
        "script": "pow(B, c)",
        "variables": [
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          "c"
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      }
    },
    {
      "id": "__intersection_4",
      "type": "operator",
      "emoji": "∩",
      "op": "intersection",
      "subexpr": "A^{c} \\cap B^{c}",
      "chartScript": {
        "script": "pow(A, c)*pow(B, c)*cap",
        "variables": [
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          "B",
          "c",
          "cap"
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      }
    }
  ],
  "edges": [
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      "to": "__union_3"
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      "to": "__power_2"
    },
    {
      "from": "c",
      "to": "__power_2",
      "role": "exp"
    },
    {
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      "to": "__equals_1"
    },
    {
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      "to": "__power_5"
    },
    {
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      "to": "__power_5",
      "role": "exp"
    },
    {
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      "to": "__intersection_4"
    },
    {
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      "to": "__power_6"
    },
    {
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      "to": "__power_6",
      "role": "exp"
    },
    {
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      "to": "__intersection_4"
    },
    {
      "from": "__intersection_4",
      "to": "__equals_1"
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  ],
  "classification": {
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}

flowchart RL
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  __power_5(("$(\cdot)^{\cdot}$")):::operator
  __power_6(("$(\cdot)^{\cdot}$")):::operator
  __intersection_4(("$\cap$")):::operator
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  B --> __union_3
  __union_3 --> __power_2
  c -->|exp| __power_2
  __power_2 --> __equals_1
  A --> __power_5
  c -->|exp| __power_5
  __power_5 --> __intersection_4
  B --> __power_6
  c -->|exp| __power_6
  __power_6 --> __intersection_4
  __intersection_4 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
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{
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      "id": "c0___forall_1",
      "type": "function",
      "latex": "\\forall",
      "op": "forall",
      "subexpr": "\\forall(x)",
      "chartScript": {
        "script": "forall(x)",
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      }
    },
    {
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    {
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      "subexpr": "{R}",
      "chartScript": {
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      }
    },
    {
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      "type": "relation",
      "label": "element of",
      "emoji": "∈",
      "op": "element_of",
      "subexpr": "\\forall(x) \\in \\mathbb{R}",
      "chartScript": {
        "script": "R*in*mathbb*forall(x)",
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      }
    },
    {
      "id": "c1___power_1",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "x^2",
      "chartScript": {
        "script": "pow(x, 2)",
        "variables": [
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      }
    },
    {
      "id": "c1___num_2",
      "type": "number",
      "label": "0",
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      "chartScript": {
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        "variables": []
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    },
    {
      "id": "c1___greater_equal_3",
      "type": "relation",
      "label": "greater than or equal to",
      "emoji": "≥",
      "op": "greater_equal",
      "subexpr": "x^2 \\geq 0",
      "chartScript": {
        "script": "pow(x, 2)",
        "variables": [
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      }
    }
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  "edges": [
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      "to": "c0___element_of_2",
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    {
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  "classification": {
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}

flowchart RL
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  c1___power_1(("${(\cdot)}^{2}$")):::operator
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  x --> c0___forall_1
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  R -->|rhs| c0___element_of_2
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  c1___power_1 -->|lhs| c1___greater_equal_3
  c1___num_2 -->|rhs| c1___greater_equal_3
  linkStyle 0 stroke:#aaa,stroke-width:2px
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{
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      "type": "function",
      "latex": "\\exists",
      "op": "exists",
      "subexpr": "\\exists(x)",
      "chartScript": {
        "script": "exists(x)",
        "variables": [
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      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
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      "chartScript": {
        "script": "x",
        "variables": [
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      }
    },
    {
      "id": "N",
      "type": "scalar",
      "latex": "\\mathbb{N}",
      "subexpr": "{N}",
      "chartScript": {
        "script": "N",
        "variables": [
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      }
    },
    {
      "id": "c0___element_of_2",
      "type": "relation",
      "label": "element of",
      "emoji": "∈",
      "op": "element_of",
      "subexpr": "\\exists(x) \\in \\mathbb{N}",
      "chartScript": {
        "script": "N*in*mathbb*exists(x)",
        "variables": [
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          "in",
          "mathbb",
          "x"
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      }
    },
    {
      "id": "c1___greater_than_1",
      "type": "relation",
      "op": "greater_than",
      "subexpr": "x > 100",
      "chartScript": {
        "script": "x - 100",
        "variables": [
          "x"
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      }
    },
    {
      "id": "c1___num_2",
      "type": "number",
      "label": "100",
      "subexpr": "100",
      "chartScript": {
        "script": "100",
        "variables": []
      }
    }
  ],
  "edges": [
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    {
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      "to": "c0___element_of_2",
      "role": "rhs"
    },
    {
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      "role": "lhs"
    },
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      "to": "c1___greater_than_1",
      "role": "rhs"
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  "classification": {
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    "count": 2,
    "clauses": [
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        "kind": "algebraic"
      },
      {
        "kind": "algebraic"
      }
    ]
  }
}

flowchart RL
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  c0___exists_1{{"$\exists(\cdot)$"}}:::function
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  c0___element_of_2{"∈"}:::relation
  c1___greater_than_1{"$>$"}:::relation
  c1___num_2["$100$"]:::number
  x --> c0___exists_1
  c0___exists_1 -->|lhs| c0___element_of_2
  N -->|rhs| c0___element_of_2
  x -->|lhs| c1___greater_than_1
  c1___num_2 -->|rhs| c1___greater_than_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
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      "id": "__neg_1",
      "type": "function",
      "latex": "\\neg",
      "op": "neg",
      "subexpr": "\\neg (P \\land Q)",
      "chartScript": {
        "script": "neg(P*Q*land)",
        "variables": [
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          "Q",
          "land"
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      }
    },
    {
      "id": "P",
      "type": "scalar",
      "latex": "P",
      "subexpr": "P",
      "chartScript": {
        "script": "P",
        "variables": [
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      }
    },
    {
      "id": "Q",
      "type": "scalar",
      "latex": "Q",
      "subexpr": "Q",
      "chartScript": {
        "script": "Q",
        "variables": [
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        ]
      }
    },
    {
      "id": "__conjunction_2",
      "type": "operator",
      "emoji": "∧",
      "op": "conjunction",
      "subexpr": "P \\land Q",
      "chartScript": {
        "script": "P*Q*land",
        "variables": [
          "P",
          "Q",
          "land"
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      }
    },
    {
      "id": "__neg_4",
      "type": "function",
      "latex": "\\neg",
      "op": "neg",
      "subexpr": "\\neg P ",
      "chartScript": {
        "script": "P*neg",
        "variables": [
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          "neg"
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      }
    },
    {
      "id": "__neg_5",
      "type": "function",
      "latex": "\\neg",
      "op": "neg",
      "subexpr": "\\neg Q ",
      "chartScript": {
        "script": "Q*neg",
        "variables": [
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          "neg"
        ]
      }
    },
    {
      "id": "__disjunction_3",
      "type": "operator",
      "emoji": "∨",
      "op": "disjunction",
      "subexpr": "\\neg P  \\lor \\neg Q ",
      "chartScript": {
        "script": "P*Q*lor*pow(neg, 2)",
        "variables": [
          "P",
          "Q",
          "lor",
          "neg"
        ]
      }
    },
    {
      "id": "__iff_6",
      "type": "operator",
      "label": "if and only if",
      "emoji": "⇔",
      "op": "iff",
      "subexpr": "\\neg (P \\land Q)  \\iff \\neg P  \\lor \\neg Q ",
      "chartScript": {
        "script": "P*Q*iff*lor*pow(neg, 2)*neg(P*Q*land)",
        "variables": [
          "P",
          "Q",
          "iff",
          "land",
          "lor",
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      }
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  "edges": [
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    },
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      "to": "__conjunction_2"
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      "to": "__neg_1"
    },
    {
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      "to": "__neg_4"
    },
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      "from": "__neg_4",
      "to": "__disjunction_3"
    },
    {
      "from": "Q",
      "to": "__neg_5"
    },
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      "to": "__disjunction_3"
    },
    {
      "from": "__neg_1",
      "to": "__iff_6"
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    {
      "from": "__disjunction_3",
      "to": "__iff_6"
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  "classification": {
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}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  __neg_4{{"$\lnot(\cdot)$"}}:::function
  __neg_5{{"$\lnot(\cdot)$"}}:::function
  __disjunction_3(("$\lor$")):::operator
  __iff_6(("$\Leftrightarrow$")):::operator
  P --> __conjunction_2
  Q --> __conjunction_2
  __conjunction_2 --> __neg_1
  P --> __neg_4
  __neg_4 --> __disjunction_3
  Q --> __neg_5
  __neg_5 --> __disjunction_3
  __neg_1 --> __iff_6
  __disjunction_3 --> __iff_6
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
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{
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      "id": "__equals_1",
      "type": "relation",
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      "chartScript": {
        "script": "-abs(A) - abs(B) + abs(A*B*cap) + abs(A*B*cup)",
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    },
    {
      "id": "__abs_2",
      "type": "function",
      "op": "abs",
      "subexpr": "\\left|{A \\cup B}\\right|"
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "A",
      "subexpr": "A",
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      }
    },
    {
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      "type": "scalar",
      "latex": "B",
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        "variables": [
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      }
    },
    {
      "id": "__union_3",
      "type": "operator",
      "emoji": "∪",
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      "subexpr": "A \\cup B",
      "chartScript": {
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        "variables": [
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          "B",
          "cup"
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      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "\\left|{A}\\right| + \\left|{B}\\right| - \\left|{A \\cap B}\\right|"
    },
    {
      "id": "__add_5",
      "type": "operator",
      "op": "add",
      "subexpr": "\\left|{A}\\right| + \\left|{B}\\right|"
    },
    {
      "id": "__abs_6",
      "type": "function",
      "op": "abs",
      "subexpr": "\\left|{A}\\right|"
    },
    {
      "id": "__abs_7",
      "type": "function",
      "op": "abs",
      "subexpr": "\\left|{B}\\right|"
    },
    {
      "id": "__negation_8",
      "type": "operator",
      "op": "negation",
      "subexpr": "-\\left|{A \\cap B}\\right|"
    },
    {
      "id": "__abs_9",
      "type": "function",
      "op": "abs",
      "subexpr": "\\left|{A \\cap B}\\right|"
    },
    {
      "id": "__intersection_10",
      "type": "operator",
      "emoji": "∩",
      "op": "intersection",
      "subexpr": "A \\cap B",
      "chartScript": {
        "script": "A*B*cap",
        "variables": [
          "A",
          "B",
          "cap"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "A",
      "to": "__union_3"
    },
    {
      "from": "B",
      "to": "__union_3"
    },
    {
      "from": "__union_3",
      "to": "__abs_2"
    },
    {
      "from": "__abs_2",
      "to": "__equals_1"
    },
    {
      "from": "A",
      "to": "__abs_6"
    },
    {
      "from": "__abs_6",
      "to": "__add_5"
    },
    {
      "from": "B",
      "to": "__abs_7"
    },
    {
      "from": "__abs_7",
      "to": "__add_5"
    },
    {
      "from": "__add_5",
      "to": "__add_4"
    },
    {
      "from": "A",
      "to": "__intersection_10"
    },
    {
      "from": "B",
      "to": "__intersection_10"
    },
    {
      "from": "__intersection_10",
      "to": "__abs_9"
    },
    {
      "from": "__abs_9",
      "to": "__negation_8"
    },
    {
      "from": "__negation_8",
      "to": "__add_4"
    },
    {
      "from": "__add_4",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __abs_2{{"$|\cdot|$"}}:::function
  A["$A$"]:::scalar
  B["$B$"]:::scalar
  __union_3(("$\cup$")):::operator
  __add_4(("$+$")):::operator
  __add_5(("$+$")):::operator
  __abs_6{{"$|\cdot|$"}}:::function
  __abs_7{{"$|\cdot|$"}}:::function
  __negation_8@{ shape: "flip-tri", label: "$-$" }
  __abs_9{{"$|\cdot|$"}}:::function
  __intersection_10(("$\cap$")):::operator
  class __negation_8 operator
  A --> __union_3
  B --> __union_3
  __union_3 --> __abs_2
  __abs_2 --> __equals_1
  A --> __abs_6
  __abs_6 --> __add_5
  B --> __abs_7
  __abs_7 --> __add_5
  __add_5 --> __add_4
  A --> __intersection_10
  B --> __intersection_10
  __intersection_10 --> __abs_9
  __abs_9 --> __negation_8
  __negation_8 --> __add_4
  __add_4 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#aaa,stroke-width:2px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#aaa,stroke-width:2px
  linkStyle 14 stroke:#aaa,stroke-width:2px