(b) Give a counter-example to show that the following statement is false. VxERVER (√x²y² ≥ 16) → (xy ≥ 4) Let P(x), Q(x), R(x), S(x) denote predicates with predicate variable x. Use the rules of inference for quantified statements to show that the following argument form is valid. vx P(x) → (Q(x) V R(x)) (premise) x R(x) → S(x) (premise) 3x~Q(x) Vx P(x) 3x S(x) (premise) (premise) (conclusion)

(b) Give a counter-example to show that the following statement is false. VxERVER (√x²y² ≥ 16) → (xy ≥ 4) Let P(x), Q(x), R(x), S(x) denote predicates with predicate variable x. Use the rules of inference for quantified statements to show that the following argument form is valid. vx P(x) → (Q(x) V R(x)) (premise) x R(x) → S(x) (premise) 3x~Q(x) Vx P(x) 3x S(x) (premise) (premise) (conclusion)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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