Question:

The proposition \(\sim(p \vee \sim q) \vee \sim(p \vee q)\) is logically equivalent to:

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Apply De Morgan's laws to each bracket and then factor out \(\sim p\).
Updated On: Nov 11, 2026
  • \(p\)
  • \(q\)
  • \(\sim p\)
  • \(\sim q\)
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The Correct Option is C

Solution and Explanation

By De Morgan: \(\sim(p \vee \sim q) = \sim p \wedge q\) and \(\sim(p \vee q) = \sim p \wedge \sim q\).
The proposition becomes \((\sim p \wedge q) \vee (\sim p \wedge \sim q) = \sim p \wedge (q \vee \sim q) = \sim p \wedge T = \sim p\).
Answer: (3) \(\sim p\)
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