Use De Morgan's law for quantified statements and the laws of propositional logie to show the following equivalences: (a) -Vr (P(r)A-Q(z)) = 3r (-P(z) V Qtr) (b) -Vr (-P(r)-Q(u)) = 3r (-P(r) A-Q(r)) (e) -ar (-P(z) V (Q(r}A¬R(a))) = (P(x) A (-Q(z) V R(x)))

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use De Morgan's law for quantified statements and the laws of propositional
logic to show the following equivalences:
(a) -Vr (P(r) A-Q()) = 3r (-P(z) v Q(r))
(b) -Vr (-P(r) Qu)) = 3r (-P(x) A-Q(a))
(c) -ar (-P(2) V (Q() A¬R(r])) = V (P(x) A (-Q(z) V R(x)))
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Transcribed Image Text:Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences: (a) -Vr (P(r) A-Q()) = 3r (-P(z) v Q(r)) (b) -Vr (-P(r) Qu)) = 3r (-P(x) A-Q(a)) (c) -ar (-P(2) V (Q() A¬R(r])) = V (P(x) A (-Q(z) V R(x))) Pages 4 to 5 of 7 70% LT en US , Ready Automatic UTF-8 99+
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