Introduction to Logic

Implication

An implication consists of a pair of sentences separated by the ⇒ operator and enclosed in parentheses. For example, the implication of p and q is (pq).

The sentence to the left of the ⇒ operator in an implication is called the antecedent, and the sentence to the right is called the consequent. For example, in the implication (pq), p is the antecedent and q is the consequent.

The truth value of an implication is false if and only if its antecedent is true and its consequent is false; otherwise, the truth value is true.

p q (pq)
1 1 1
1 0 0
0 1 1
0 0 1

This semantics for the ⇒ operator is called material implication to distinguish it from other possibilities.


TextSection 2.2, Section 2.3
ExercisesExercise 2.1, Exercise 2.2