GATE CS 2015 Set 2 — Question 11
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Engineering Mathematics → Mathematical Logic → Propositional Logic
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Question
Consider the following two statements.
: If a candidate is known to be corrupt, then he will not be elected
: If a candidate is kind, he will be electedWhich one of the following statements follows from and as per sound inference rules of logic?
: If a candidate is known to be corrupt, then he will not be elected
: If a candidate is kind, he will be electedWhich one of the following statements follows from and as per sound inference rules of logic?
Correct answer
(C) If a person is kind, he is not known to be corrupt
Solution
Let the propositions be:
: Candidate is known to be corrupt
: Candidate will be elected
: Candidate is kindThe given statements are:
From , the contrapositive is .
Using hypothetical syllogism on () and the contrapositive of (), we get:
(If a candidate is known to be corrupt, he is not kind).The contrapositive of this derived statement () is:
(If a candidate is kind, he is not known to be corrupt).This matches option (C).
: Candidate is known to be corrupt
: Candidate will be elected
: Candidate is kindThe given statements are:
From , the contrapositive is .
Using hypothetical syllogism on () and the contrapositive of (), we get:
(If a candidate is known to be corrupt, he is not kind).The contrapositive of this derived statement () is:
(If a candidate is kind, he is not known to be corrupt).This matches option (C).
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