AMSCO'S Geometry. New York - Rye High School

62 Logicp: Angle A and B are congruent. Trueq: Angle A and B are both right angles. Falsep → q: If A and B are congruent, then A and Bare both right angles.T → F is Fp: Angle A and B are not congruent. Falseq: Angle A and B are not both right angles. Truep → q: If A and B are not congruent, then A and Bare not both right angles.F → T is TAgain, the conditional and the inverse have opposite truth values.3. A conditional and its inverse can have the same truth value.Let r represent “Twice Talia’s age is 10.”Let q represent “Talia is 5 years old.”Conditional If twice Talia’s age is 10, then Talia is 5 years old.(r → s):frInverse If twice Talia’s age is not 10, then Talia is not 5 years old.(r → s):grefWhen Talia is 5, r is true and s is true. The conditional is true.When Talia is 5, r is false and s is false. The inverse is true.Both the conditional and its inverse have the same truth value.When Talia is 6, r is false and s is false. The conditional is true.When Talia is 6, r is true and s is true. The conditional is true.Again, the conditional and its inverse have the same truth value.ssThese three illustrations allow us to make the following conclusion: A conditional (p → q) and its inverse (p → q) may or may not have thesame truth value.This conclusion can be shown in the truth table. Note that the conditional(p → q) and its inverse (p → q) have the same truth value when p and q havethe same truth value. The conditional (p → q) and its inverse (p → q) haveopposite truth values when p and q have opposite truth values.ConditionalInversep q p q p → q p → qT T F F T TT F F T F TF T T F T FF F T T T T