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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) ((P⇒Q₁) ^ (P⇒ Q₂)) → (P⇒ (Q₁ ^ Q₂)) (b) (( € D. P(z) V Q(x)) ⇒ R(y)) → (((ªr € D. P(x)) ⇒ R(y)) ^ ((x € 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) ((P⇒Q₁) ^ (P⇒ Q₂)) → (P⇒ (Q₁ ^ Q₂)) (b) (( € D. P(z) V Q(x)) ⇒ R(y)) → (((ªr € D. P(x)) ⇒ R(y)) ^ ((x € 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) A (P⇒ Q₂)) ⇒(P⇒ (Q1 ^ Q2)) (b) ((x € D, P(z) 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) A (P⇒ Q₂)) ⇒(P⇒ (Q1 ^ Q2)) (b) ((x € D, P(z) v Q(x)) ⇒ R(y)) ⇒ (((3x € D, P(x)) ⇒ R(y)) ^ ((3x € D, Q(x)) ⇒ R(y)))
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