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Answer: Verified; columns 5, 7 and 8 of the truth table are identical.

\(p\)\(q\)\(\sim q\)\(p \rightarrow \sim q\)\(\sim(p \rightarrow \sim q)\)\(\sim(\sim q)\)\(p \wedge \sim(\sim q)\)\(p \wedge q\)
TTFFTTTT
TFTTFFFF
FTFTFTFF
FFTTFFFF

The columns of \(\sim(p \rightarrow \sim q)\), \(p \wedge \sim(\sim q)\) and \(p \wedge q\) are identical (T, F, F, F). Hence \(\sim(p \rightarrow \sim q) \equiv p \wedge \sim(\sim q) \equiv p \wedge q\).

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