Using truth table, examine whether the following statement pattern is a tautology, a contradiction or a contingency.\((p\wedge\sim q)\to(\sim p\wedge\sim q)\)

Q.2 (A) (i) Using truth table, examine whether the following statement pattern is a tautology, a contradiction or a contingency.

\((p\wedge\sim q)\to(\sim p\wedge\sim q)\)

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: The statement pattern is a contingency.

p	q	\(\sim p\)	\(\sim q\)	\(p\wedge\sim q\)	\(\sim p\wedge\sim q\)	\((p\wedge\sim q)\to(\sim p\wedge\sim q)\)
T	T	F	F	F	F	T
T	F	F	T	T	F	F
F	T	T	F	F	F	T
F	F	T	T	F	T	T

The last column contains both T and F (it is F only in the second row, where \(p\wedge\sim q\) is true and \(\sim p\wedge\sim q\) is false). Hence the given statement pattern is a contingency.

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Using truth table, examine whether the following statement pattern is a tautology, a contradiction or a contingency.\((p\wedge\sim q)\to(\sim p\wedge\sim q)\)

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