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4. Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. a. (p^¬q) V ¬(p V q) and ¬q b. -p → ¬(q v r) and (q → p) A (r → p) c. -(p v (¬q ^ (r → p))) and ¬p ^ (¬r → q)

4. Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. a. (p^¬q) V ¬(p V q) and ¬q b. -p → ¬(q v r) and (q → p) A (r → p) c. -(p v (¬q ^ (r → p))) and ¬p ^ (¬r → q)

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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Part II: Proving logical equivalence using laws of propositional logic 4. Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. a. (pA¬q) V ¬(p V q) and ¬q b. -p → -(q v r) and (q → p) ^ (r → p) c. ¬(p v (¬q ^ (r → p))) and ¬p ^ (¬r → q) d. p+ q and (p ^ q) V (¬p ^ ¬q)
Transcribed Image Text:Part II: Proving logical equivalence using laws of propositional logic 4. Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. a. (pA¬q) V ¬(p V q) and ¬q b. -p → -(q v r) and (q → p) ^ (r → p) c. ¬(p v (¬q ^ (r → p))) and ¬p ^ (¬r → q) d. p+ q and (p ^ q) V (¬p ^ ¬q)
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