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31. Show that p→q and (p →q) ^ (q→p) are logically equivalent.

31. Show that p→q and (p →q) ^ (q→p) are logically equivalent.

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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31. Show that p→q and (p →q) ^ (q→p) are logically equivalent.
Transcribed Image Text:31. Show that p→q and (p →q) ^ (q→p) are logically equivalent.
19. Determine whether (-q ^ (p →q)) → ¬p is a tautology. Each of Exercises 20-32 asks you to show that two compound propositions are logically equivalent. To do this, either show that both sides are true, or that both sides are false, for ex- actly the same combinations of truth values of the proposi- tional variables in these expressions (whichever is easier).
Transcribed Image Text:19. Determine whether (-q ^ (p →q)) → ¬p is a tautology. Each of Exercises 20-32 asks you to show that two compound propositions are logically equivalent. To do this, either show that both sides are true, or that both sides are false, for ex- actly the same combinations of truth values of the proposi- tional variables in these expressions (whichever is easier).
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