Question:

The statement \(\sim(p\leftrightarrow\sim q)\) is :

Show Hint

\(p\leftrightarrow\sim q\) is the negation of \(p\leftrightarrow q\); negating again returns \(p\leftrightarrow q\).
Updated On: Nov 11, 2026
  • a tautology
  • a fallacy
  • equivalent to \(p\leftrightarrow q\)
  • equivalent to \(\sim p\leftrightarrow q\)
Show Solution
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The Correct Option is C

Solution and Explanation

Truth table:
pq~qp ↔ ~q~(p ↔ ~q)p ↔ q
TTFFTT
TFTTFF
FTFTFF
FFTFTT
The column of \(\sim(p\leftrightarrow\sim q)\) is T, F, F, T: neither all T nor all F, so options (1) and (2) are wrong. It matches \(p\leftrightarrow q\) exactly. Option (4), \(\sim p\leftrightarrow q\), has values F, T, T, F, which differs.
Answer: (3) equivalent to \(p\leftrightarrow q\)
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