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Question

The contrapositive of the statement ‘ If it is a Friday or if the sky is clear, then Sam plays’ is ___.

A
If Sam plays, then it is a friday or the sky is clear
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B
If Sam does not play, then it is a Friday or the sky is clear
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C
If Sam does not play, then it is not a Friday and the sky is not clear
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D
If Sam does not play, then it is a Friday or the sky is not clear
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Solution

The correct option is C If Sam does not play, then it is not a Friday and the sky is not clear
The contrapositive of pq is qp.
p: It is a Friday
q: The sky is clear
r: Sam plays
The given statement is (pq)r. Its contrapositive is r(p q). Also, (p q)=p q. Hence, the contrapositive of the given statement is rp q
This can be translated as ‘If Sam does not play, then it is not a Friday and the sky is not clear’.

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