For primitive statements p, q, and r, let P denote the statement
[p ∧ (q ∧ r)] ∨ ¬[p ∨ (q ∧ r)],
while P1 denotes the statement
[P ∧ (q ∨ r)] ∨ ¬[p ∨ (q ∨ r)].
(a) Use the rules of inference to show that
q ∧ r ⇒ q ∨ r.
(b) Is it true that P ⇒ P1?