High Quality Content by WIKIPEDIA articles! The material conditional, also known as material implication, is a binary truth function -> such that the compound sentence p->q (typically read "if p then q") is logically equivalent to the negative compound: not(p and not q). A material conditional compound itself is often simply called a conditional. By definition of "->", the compound p->q is false if and only if both p is true and q is false. That is to say that p->q is true if and only if either p is false or q is true (or both). Thus -> is a function from pairs of truth values of the components p, q to truth values of the compound p->q, whose truth value is entirely a function of the truth values of the components. Thus p->q is said to be truth-functional. p->q is logically equivalent also to ¬p q (either not p, or q (or both)), and to ¬q -> ¬p (if not q then not p), but not to ¬p -> ¬q. For convenience, p->q is typically read "If p, then q", "p only if q", or "q if p". Saying "It is false that if p then q" does not always sound logically equivalent in everyday English to saying "both p and not q" but, when used in logic, it is taken as logically equivalent.

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