Q.15 Examine whether the statement pattern \((p \wedge q) \wedge (\sim p \vee \sim q)\) is a tautology or contradiction or contingency.
Best answer
Answer: It is a contradiction.
| \(p\) | \(q\) | \(p \wedge q\) | \(\sim p\) | \(\sim q\) | \(\sim p \vee \sim q\) | \((p \wedge q) \wedge (\sim p \vee \sim q)\) |
|---|---|---|---|---|---|---|
| T | T | T | F | F | F | F |
| T | F | F | F | T | T | F |
| F | T | F | T | F | T | F |
| F | F | F | T | T | T | F |
All entries in the last column are F, so the statement pattern is a contradiction. (Indeed \(\sim p \vee \sim q \equiv \sim(p \wedge q)\), so the pattern is of the form \(s \wedge \sim s\).)
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