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Q.

What is negation of the compound proposition? If the examination is difficult, then I shall pass if I study hard.

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a

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

b

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

c

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

d

None of these

answer is A.

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Detailed Solution

If p : Examination is difficult q : I shall pass  r : I study hard Given result is p⇒(r⇒q) Now, ~(r⇒q)=r∧~q~(p⇒(r⇒q))≡p∧(r∧~q)The examination is difficult and I study hard but I shall not pass.
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