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  2. 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]

  3. Material implication (rule of inference) - Wikipedia

    en.wikipedia.org/wiki/Material_implication_(rule...

    The rule states that P implies Q is logically equivalent to not-or and that either form can replace the other in logical proofs. In other words, if P {\displaystyle P} is true, then Q {\displaystyle Q} must also be true, while if Q {\displaystyle Q} is not true, then P {\displaystyle P} cannot be true either; additionally, when P {\displaystyle ...

  4. Truth value - Wikipedia

    en.wikipedia.org/wiki/Truth_value

    Logical biconditional becomes the equality binary relation, and negation becomes a bijection which permutes true and false. Conjunction and disjunction are dual with respect to negation, which is expressed by De Morgan's laws: ¬(pq) ⇔ ¬ p ∨ ¬ q ¬(pq) ⇔ ¬ p ∧ ¬ q. Propositional variables become variables in the Boolean ...

  5. Necessity and sufficiency - Wikipedia

    en.wikipedia.org/wiki/Necessity_and_sufficiency

    The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false". [9] [1] By contraposition, this is the same thing as "whenever P is true, so is Q". The logical relation between P and Q is expressed as "if P, then Q" and denoted "PQ" (P implies Q).

  6. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    Some of these connectives may be defined in terms of others: for instance, implication, pq, may be defined in terms of disjunction and negation, as ¬pq; [71] and disjunction may be defined in terms of negation and conjunction, as ¬(¬p ∧ ¬q). [48]

  7. Propositional variable - Wikipedia

    en.wikipedia.org/wiki/Propositional_variable

    In mathematical logic, a propositional variable (also called a sentence letter, [1] sentential variable, or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics.

  8. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    The simplest case occurs when an OR formula becomes one its own inputs e.g. p = q. Begin with (p ∨ s) = q, then let p = q. Observe that q's "definition" depends on itself "q" as well as on "s" and the OR connective; this definition of q is thus impredicative. Either of two conditions can result: [24] oscillation or memory.

  9. Three-valued logic - Wikipedia

    en.wikipedia.org/wiki/Three-valued_logic

    It may be defined either by appending one of the two equivalent axioms (¬qp) → (((pq) → p) → p) or equivalently p∨(¬q)∨(pq) to the axioms of intuitionistic logic, or by explicit truth tables for its operations. In particular, conjunction and disjunction are the same as for Kleene's and Ɓukasiewicz's logic, while the ...