Using the truth table, verify \(p\vee(q\wedge r)\equiv(p\vee q)\wedge(p\vee r)\)
Q.3 (B) (i) Using the truth table, verify \(p\vee(q\wedge r)\equiv(p\vee q)\wedge(p\vee r)\)
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Answer: Verified (columns 5 and 8 are identical).
| p | q | r | \(q\wedge r\) | \(p\vee(q\wedge r)\) | \(p\vee q\) | \(p\vee r\) | \((p\vee q)\wedge(p\vee r)\) |
|---|---|---|---|---|---|---|---|
| T | T | T | T | T | T | T | T |
| T | T | F | F | T | T | T | T |
| T | F | T | F | T | T | T | T |
| T | F | F | F | T | T | T | T |
| F | T | T | T | T | T | T | T |
| F | T | F | F | F | T | F | F |
| F | F | T | F | F | F | T | F |
| F | F | F | F | F | F | F | F |
The columns of \(p\vee(q\wedge r)\) and \((p\vee q)\wedge(p\vee r)\) have the same truth values in every row. Hence \(p\vee(q\wedge r)\equiv(p\vee q)\wedge(p\vee r)\).
Doubtly AI
· 28 Oct 2026
AI-verified · Oct 2026
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