Logic

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  • Conjunctive normal form (CNF)
    Last edited: 2023-11-11

    A Boolean function is in conjunctive normal form if it is a collection of or statements unified by and operations. The or statements can contain negated variables but no further nesting.

    The following are in CNF:

    • $A$,
    • $(A \lor B)$,
    • $(A) \land (B)$,
    • $(A \lor B) \land (A)$,
    • $\lnot A$ , and
    • $(A \lor \lnot B \lor \lnot C) \land (\lnot D \lor E \lor F)$.

    The following are not in CNFL:

  • Exclusive or
    Last edited: 2026-02-05

    Exclusive or

    Exclusive or (Xor) is a binary operation where exactly on of the inputs needs to be true

  • Logical and
    Last edited: 2026-02-05

    Logical and

    This is a boolean function regularly expressed as $\land: \{T, F\}^2 \rightarrow \{T, F\}$ which is only true if both its inputs are.

  • Logical OR
    Last edited: 2026-02-05

    Logical OR

    This is a boolean function typically expressed as $\lor: \{T, F\}^2 \rightarrow \{T, F\}$ which is only false if both its inputs are.