Mathematical Reasoning * — JEE Main · 2021 · 25 Jul 2021 · Shift 2 Question with Solution

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :

(A)The match will not be played or weather is good and ground is not wet.
(B)The match will not be played or weather is not good and ground is wet.
(C)If the match will not be played, then either weather is not good or ground is wet.
(D)The match will be played and weather is not good or ground is wet.✓ Correct

Answer: (D)

Solution

Write

p

for “the match will be played”,

q

for “the weather is good” and

r

for “the ground is not wet”. The connective “only if” makes the statement

p \to (q \land r)

, and

\sim (p \to (q \land r)) \equiv p \land \sim (q \land r) \equiv p \land (\sim q \lor \sim r)

In words: the match will be played and the weather is not good or the ground is wet.

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option