Question:

If \(p \rightarrow (p \wedge \sim q)\) is false, then the truth values of p and q are respectively :

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An implication \(A \rightarrow B\) is false only when A is true and B is false.
Updated On: Nov 5, 2026
  • T, T
  • T, F
  • F, T
  • F, F
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The Correct Option is A

Solution and Explanation

\(p \rightarrow (p \wedge \sim q)\) is false only when the antecedent p is true and the consequent \(p \wedge \sim q\) is false.
So \(p = T\). With \(p = T\), \(p \wedge \sim q\) has the truth value of \(\sim q\). For it to be false, \(\sim q = F\), so \(q = T\).
Thus p and q are T and T respectively.
Answer: (1) T, T
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