Determine whether (p→g) ^ (p Vr) and -p V (q^r) are two logically equivalent propositions.
Determine whether (p→g) ^ (p Vr) and -p V (q^r) are two logically equivalent propositions.
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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Transcribed Image Text:Determine whether (p→g) ^(-p Vr) and p V (q^r)
are two logically equivalent propositions.
Expert Solution
Step 1
Given that
Here we need to prove both logics are equivalent.
For that we construct truth table.
| p | q | r | ||||||
| T | T | T | F | T | T | T | T | T |
| T | T | F | F | T | F | T | F | T |
| T | F | T | F | F | T | T | F | T |
| T | F | F | F | F | F | T | F | T |
| F | T | T | T | T | T | F | T | F |
| F | T | F | T | T | T | F | F | F |
| F | F | T | T | T | T | F | F | F |
| F | F | F | T | T | T | T | F | T |
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