Question

The simplified form of [(~ p v q) ∧ r] v [(p ∧ ~ q) ∧ r] is ______.

Options

• p

• q

• r

• p ∧ q

Answer 1

The simplified form of [(~ p v q) ∧ r] v [(p ∧ ~ q) ∧ r] is r.

Explanation:

[(~p v q) ∧ r] v [(p ∧ ~q) ∧ r] 

= [~(p ∧ ~q) ∧ r] v [(p ∧ ~q) ∧ r]   ...(Rule of negation)

= [~(p ∧ ~q) v (p ∧ ~q)] ∧ r    ...(Distributive law)

= T ∧ r    ...(Complement law)

= r   ...(Identity law)