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Let p,q,r 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?

my answer: (¬p∧r)∨((p∧q)→¬r) this question was from one of the entrance exam GATE, there answer key shows (¬p∧r)∧(¬r→(p∧q)) as answer.

it would helpful for me if anyone can point out what I'm doing wrong here

Andrés E. Caicedo
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jt26
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  • We can't point out what you're doing wrong, because you don't show us all the work you did to arrive at your answer. – amWhy Oct 22 '17 at 16:22

1 Answers1

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It says that it is "not pleasant only if it is raining and it is cold.”

"Only if" is not the same as if; it could be rewritten as "only when". This sentence means that if it is not pleasant, this can only happen if it is raining and cold. As in if unpleasant, then raining. i.e. (¬r→(p∧q)).

The first part you got right. And in between the two sentences, they said "and" so it would be ^. Thus, (¬p∧r)∧(¬r→(p∧q))

ions me
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  • "p only if q," is the same as "if p then q"; it is not the same as "if". That is, "p if q" means "if q then p". I see that you got things right, so we're likely on the same page with his; I just want to make things as explicit as possible for the asker. – amWhy Oct 22 '17 at 16:24