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?
- A.
If a person is known to be corrupt, he is kind
- B.
If a person is not known to be corrupt, he is not kind
- C.
If a person is kind, he is not known to be corrupt
- 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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