GATE CS 2017 Set 2 — Question 11
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Engineering Mathematics → Mathematical Logic → Propositional Logic
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Question
Let denote the statements "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
Correct answer
(A) (¬ p ∧ r) ∧ (¬ r arrow (p ∧ q))
Solution
Let = "It is raining", = "It is cold", = "It is pleasant".The sentence has two parts joined by "and":
1."It is not raining and it is pleasant" .
2."It is not pleasant only if it is raining and it is cold". The pattern " only if " means
Joining them: , which is option (A) exactly.Why the others are not the translation:X → Y, so this is .- (B) writes the second part as , i.e. "it is not pleasant if it is raining and cold", the converse direction of "only if". (Whenever holds, both second parts happen to be true, so (A) and (B) have the same truth table, but (B) is not a translation of the sentence.)
- (C) and (D) join the two parts with , but the sentence joins them with "and".
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