GATE 2017 CS (CS2) – Question 21

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 1 mark · Multiple choice

Let p,q,r mean “It is raining”, “It is cold”, “It is pleasant”. Represent: “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold.”

$(\neg p\land r)\land(\neg r\to(p\land q))$
$(\neg p\land r)\land((p\land q)\to\neg r)$
$(\neg p\land r)\lor((p\land q)\to\neg r)$
$(\neg p\land r)\lor(\neg r\to(p\land q))$

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Show answer and explanation

Correct answer: (A) $(\neg p\land r)\land(\neg r\to(p\land q))$

Explanation

The first clause is ¬p∧r. “A only if B” translates A→B, so the second clause is ¬r→(p∧q). The word “and” joins the clauses by conjunction. This yields option A.

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