Question:

For any two statements p and q, the negation of the expression p∨(∼p∧q) is:

Updated On: Mar 31, 2026
  • p∧q

  • p↔q

  • ∼p∨∼q

  • ∼p∧∼q
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The Correct Option is D

Solution and Explanation

Explanation:
The given expression is p∨(∼p∧q).
Thus, the negation of this expression can be written as:∼(p∨(∼p∧q))
=∼p∧∼(∼p∧q)[∵∼(a∨b)≡∼a∧∼b]
=∼p∧(p∨∼q)[∵∼(a∧b)≡∼a∨∼b]
=(∼p∧p)∨(∼p∧∼q)[∵c∧(a∨b)≡(c∧a)∨(c∧b)]
=F∨(∼p∧∼q)[∵∼a∧a≡F]
=(∼p∧∼q)[∵F∨a≡a]
Hence, the correct option is (D).
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Concepts Used:

Sets

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Cardinal Number of a Set:

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