implication

implication

Logic

a. the operator that forms a sentence from two given sentences and corresponds to the English if … then …

b. a sentence so formed. Usually written p→q or p⊃q, where p,q are the component sentences, it is true except when p (the antecedent) is true and q (the consequent) is false

c. the relation between such sentences

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

implication

[‚im·plə′kā·shən]

(mathematics)

The logical relation between two statements p and q, usually expressed as “if p then q.“

A logic operator having the characteristic that if p and q are statements, the implication of p and q is false if p is true and q is false, and is true otherwise. Also known as conditional implication; if-then operation; material implication.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.