Question

The negation of the statement pattern ~ p v(q → ~ r) is ______.

Options

• p ∧ (q ∧ r)

• ~ p ∧ (q ∧ r)

• p ∨ (q ∧ r)

• p → (q ∧ ~ r)

Answer 1

The negation of the statement pattern ~ p v( q → ~ r) is p ∧ (q ∧ r).

Explanation:

We have,

~ p v (q → ~ r)

~ p v (~ q → ~ r)   ...[∵ p → q = ~ p v q]

~ p v ~ (q ∧ r)

~ (p ∧ (q ∧ r))

∴ ~ (~ (p ∧ (q ∧ r))

p ∧ (q ∧ r)