Question

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

• A. p∧q
• B. p↔q
• C. ∼p∨∼q
• D. ∼p∧∼q

Answer 1

Answer: (D)

∼p∧∼q

Answer 2

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).