Consider the following two statements. 𝑆1: If a candidate is known to be…

2015

Consider the following two 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?

  1. A.

    If a person is known to be corrupt, he is kind

  2. B.

    If a person is not known to be corrupt, he is not kind

  3. C.

    If a person is kind, he is not known to be corrupt

  4. D.

    If a person is not kind, he is not known to be corrupt

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Correct answer: C

Given 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.

Reasoning:

  • Take the contrapositive of S1: if a candidate is elected, then he is not known to be corrupt.

  • From S2: if a candidate is kind, then he is elected.

  • Chain the implications: if a candidate is kind, then he is elected; and if he is elected, then he is not known to be corrupt. Therefore if a candidate is kind, then he is not known to be corrupt.

Conclusion: The statement 'If a person is kind, he is not known to be corrupt' follows validly from the given premises. The other choices either reverse or negate the implications and are not logically implied.

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