Question

Consider the following statements :

P : Suman is brilliant

Q : Suman is rich.

R : Suman is honest

the negation of the statement

“Suman is brilliant and dishonest if and only if suman is rich” can be equivalently expressed as :

(1) ~ Q ↔ ~ P v R

(2) ~ Q ↔ ~ P ∧ R

(3) ~ Q ↔ P v ~R

(4) ~ Q ↔ P ∧~R

Answer 1

Correct option (4) ~ Q ↔ P ∧~R

Explanation:

Given statement is equal to (p ∧ ~ R) ↔ Q Negation of the above statement is ~ Q ↔ (p ∧ ~R) ~ Q ↔ p ∧ ~ R