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Logic-Gates-and-operators
September 20, 2024Match-the-following
September 21, 2024GATE 2015 [Set-2]
| Question 16 |
Consider the following statements:
-
S1: If a candidate is known to be corrupt, then he will not be elected.
S2: If a candidate is kind, he will be elected.
Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?
| If a person is known to corrupt, he is kind | |
| If a person is not known to be corrupt, he is not kind
| |
| If a person is kind, he is not known to be corrupt
| |
| If a person is not kind, he is not known to be corrupt |
Question 16 Explanation:
Let p: candidate known to be corrupt
q: candidate will be elected
r: candidate is kind
then S1 = p→~q
= q→~p (conrapositive rule)
and S2: r→q ⇒ r→~p (transitive rule)
i.e., If a person is kind, he is not known to be corrupt.
∴ Option is C
q: candidate will be elected
r: candidate is kind
then S1 = p→~q
= q→~p (conrapositive rule)
and S2: r→q ⇒ r→~p (transitive rule)
i.e., If a person is kind, he is not known to be corrupt.
∴ Option is C
Correct Answer: C
Question 16 Explanation:
Let p: candidate known to be corrupt
q: candidate will be elected
r: candidate is kind
then S1 = p→~q
= q→~p (conrapositive rule)
and S2: r→q ⇒ r→~p (transitive rule)
i.e., If a person is kind, he is not known to be corrupt.
∴ Option is C
q: candidate will be elected
r: candidate is kind
then S1 = p→~q
= q→~p (conrapositive rule)
and S2: r→q ⇒ r→~p (transitive rule)
i.e., If a person is kind, he is not known to be corrupt.
∴ Option is C
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