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Question

Negation of the compound proposition: If the examination is difficult, then I shall pass if I study hard


A

The examination is difficult and I study hard and I shall pass

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B

The examination is difficult and I study hard but I shall not pass

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C

The examination is not difficult and I study hard and I shall pass

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D

None of these

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Solution

The correct option is B

The examination is difficult and I study hard but I shall not pass


Explanation for the correct option:

Finding the negation of the compound proposition:

Let p: examination is difficult

q: I shall pass

r: I study hard

p(rq)

~(rq)=r~q

~(p(rq))p(r~q)

The examination is difficult and I study hard but I shall not pass.

Hence, the correct answer is Option (B).


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