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The negation of p ∧ ( q → ∼ r ) is

Options

  1. A∼ p ∧ q ∧ r
  2. B  p ∨ ( q ∨ r )
  3. C  p ∨ ( q ∧ r )
  4. D∼ p ∨ ( q ∧ r )

Correct answer

D. ∼ p ∨ ( q ∧ r )

Step-by-step solution

∼ p ∧ q → ∼ r = ∼ p ∨ ∼ q → ∼ r ( ∵ ~ ( p ∧ q ) = ~ p ∨ ~ q & ~ ( p → q ) = p ∧ ~ q ) = ∼ p ∨ ( q ∧ ∼ ( ∼ r ) ) = ∼ p ∨ ( q ∧ r )

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