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
The atomic statements are:
Here, is "it is not pleasant" () and is "it is raining and it is cold" ().
So, this part translates to .Combining both parts with the conjunction "and":
- : "It is raining"
- : "It is cold"
- : "It is pleasant"
1.Part 1: "It is not raining and it is pleasant" translates to .
2.Part 2: "it is not pleasant only if it is raining and it is cold".
Recall the logical rule: " only if " is equivalent to A → B.Here, is "it is not pleasant" () and is "it is raining and it is cold" ().
So, this part translates to .Combining both parts with the conjunction "and":
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