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  2. Boolean satisfiability problem - Wikipedia

    en.wikipedia.org/wiki/Boolean_satisfiability_problem

    Another variant is the not-all-equal 3-satisfiability problem (also called NAE3SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine if an assignment to the variables exists such that in no clause all three literals have the same truth value.

  3. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false. n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number . ⊕

  4. If and only if - Wikipedia

    en.wikipedia.org/wiki/If_and_only_if

    The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...

  5. Necessity and sufficiency - Wikipedia

    en.wikipedia.org/wiki/Necessity_and_sufficiency

    For a third facet, identify every mathematical predicate N with the set T(N) of objects, events, or statements for which N holds true; then asserting the necessity of N for S is equivalent to claiming that T(N) is a superset of T(S), while asserting the sufficiency of S for N is equivalent to claiming that T(S) is a subset of T(N).

  6. Logical equivalence - Wikipedia

    en.wikipedia.org/wiki/Logical_equivalence

    This statement expresses the idea "' if and only if '". In particular, the truth value of p ↔ q {\displaystyle p\leftrightarrow q} can change from one model to another. On the other hand, the claim that two formulas are logically equivalent is a statement in metalanguage , which expresses a relationship between two statements p {\displaystyle ...

  7. Logical equality - Wikipedia

    en.wikipedia.org/wiki/Logical_equality

    Logical equality is a logical operator that compares two truth values, or more generally, two formulas, such that it gives the value True if both arguments have the same truth value, and False if they are different.

  8. Help:Conditional expressions - Wikipedia

    en.wikipedia.org/wiki/Help:Conditional_expressions

    See also: the {{}} template. The #if function selects one of two alternatives based on the truth value of a test string. {{#if: test string | value if true | value if false}} As explained above, a string is considered true if it contains at least one non-whitespace character.

  9. Truth table - Wikipedia

    en.wikipedia.org/wiki/Truth_table

    A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]