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5. Prove that the following equivalences are tautology. Show your work in detail. For each step, you must clearly state which rule you apply. (a) ((PQ₁) ^ (P⇒ Q2)) → (P⇒ (Q1 ^ Q2)) (b) ((3x = D. P(x) VQ(x)) = R(y)) (((x € D, P(x)) = R(y)) ^ ((3 D. Q(x)) = R(y)))

5. Prove that the following equivalences are tautology. Show your work in detail. For each step, you must clearly state which rule you apply. (a) ((PQ₁) ^ (P⇒ Q2)) → (P⇒ (Q1 ^ Q2)) (b) ((3x = D. P(x) VQ(x)) = R(y)) (((x € D, P(x)) = R(y)) ^ ((3 D. Q(x)) = R(y)))

Advanced Engineering Mathematics
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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5. Prove that the following equivalences are tautology. Show your work in detail. For each step, you must clearly state which rule you apply. (a) ((PQ₁) ^ (P⇒ Q2)) ⇒(P⇒ (Q₁ ^ Q₂)) (b) ((3x D, P(x) v Q(x)) = R(y)) (((3x D, P(x)) = R(y)) ^ ((3x D, Q(x)) = R(y)))
Transcribed Image Text:5. Prove that the following equivalences are tautology. Show your work in detail. For each step, you must clearly state which rule you apply. (a) ((PQ₁) ^ (P⇒ Q2)) ⇒(P⇒ (Q₁ ^ Q₂)) (b) ((3x D, P(x) v Q(x)) = R(y)) (((3x D, P(x)) = R(y)) ^ ((3x D, Q(x)) = R(y)))
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