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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 and I shall pass 

b

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

c

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