Question

The statement pattern p ∧ ( q v ~ p) is equivalent to ______.

Options

• p ∧ q

• q ∧ ~ p

• p v q

• p → q

Answer 1

The statement pattern p ∧ ( q v ~ p) is equivalent to p ∧ q.

Explanation:

Given statement pattern,

p ∧ ( q v ~ p)

By distributive law,

(p ∧ q) v (p ∧ ~ p)(p ∧ q) v c    ....[∵ c is contradiction]

p ∧ q