Let p, q, r denote the statement \”It is raining\”, \”It is cold\”, and \”It is pleasant\”, respectively. Then the statement \”It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold\” is represented by:
(A)
(¬ p ∧ r) ∧ ((¬ r → (p ∧ q))
(B)
(¬ p ∧ r) ∧ ((p ∧ q) → ¬ r)
(C)
(¬ p ∧ r) ∨ ((p ∧ q) → ¬ r)
(D)
(¬ p ∧ r) ∨ ((r → (p ∧ q))
Answer: (A)
Explanation:
It is not raining (~p) and it is pleasant (r) : (¬p ∧ r) It is raining (p) and it is cold (q) : (p∧q) it is not pleasant (¬r) only if it is raining and it is cold : ¬r → (p∧q) So the answer should be- (¬ p ∧ r) ∧ ((¬ r → (p ∧ q)) So, option (A) is true.
Quiz of this Question
Please comment below if you find anything wrong in the above post