​ The Boolean expression (p ⇒ q) ^ (q ⇒ ~ p) is equivalent to : (1) ~q (2) q (3) p (4) ~p ​

Question

The Boolean expression (p \(\Rightarrow\) q) ^ (q \(\Rightarrow\) ~ p) is equivalent to : 

(1) ~q 

(2) q 

(3) p 

(4) ~p

Answer 1

Correct option (4) ~p

(p → q) ^ (q → ~p) 

≡ (~p \(\lor\) q) ∧ (~q \(\lor\) ~p) {p → q ≡ ~p → q}  

≡ (~p \(\lor\) q) ∧ (~p \(\lor\) ~q) {commutative property} 

≡ ~p \(\lor\) (q ^ ~q) {distributive property} 

≡ ~p