(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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Plz solve both parts
Transcribed Image Text:Question 2
(a)
(b)
Give a counter-example to show that the following statement is false.
VxERVY ER (√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)
Vx R(x) → S(x)
-
(premise)
3x~Q(x)
Vx P(x)
3x S(x)
(premise)
(premise)
(conclusion)
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