Chapter: Mathematical Logic· Mathematics & Statistics (Commerce) Part 1

Examine whether the following statement pattern is tautology, a contradiction or a contingency. \(\sim p \rightarrow (p \rightarrow \sim q)\)

Q.2 (A)(i) Examine whether the following statement pattern is tautology, a contradiction or a contingency. \(\sim p \rightarrow (p \rightarrow \sim q)\)

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Answer: Tautology

\(p\)	\(q\)	\(\sim p\)	\(\sim q\)	\(p \rightarrow \sim q\)	\(\sim p \rightarrow (p \rightarrow \sim q)\)
T	T	F	F	F	T
T	F	F	T	T	T
F	T	T	F	T	T
F	F	T	T	T	T

All entries in the last column are T, so the statement pattern is a tautology. (Whenever \(\sim p\) is true, \(p\) is false, which makes \(p \rightarrow \sim q\) true.)

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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Examine whether the following statement pattern is tautology, a contradiction or a contingency. \(\sim p \rightarrow (p \rightarrow \sim q)\)

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