IMPLICATION

Definition : An implication, symbolized by p→q, is an if-then statement in which p  is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol →. The conditional is defined to be true unless  a true hypothesis leads to a false conclusion. A truth table for p→q is shown below. Example 1: Given: p: I do my homework. q: I get my allowance. Problem: What does p→q represent? Solution: In Example 1, p represents, "I do my homework," and q represents "I get my  allowance." The statement p→q is a conditional statement which represents  "If p, then q. p q p→q T T T T F F F T T F F T Example 2: Given: a: The sun is made of gas. b: 3 is a prime number. Problem: Write a→b as a sentence. Then construct a truth table for this conditional. Solution: The conditional a→b represents "If the sun is made of gas, then  3 is a prime number." a b a→b T T T T F F F T T F F T Example 3: Given: r: 8 is an odd number. false s: 9 is composite. true Problem: What is the truth value of  r→s? Solution:Since hypothesis r is false and conclusion s is true,the implication r→ s