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Question

Consider the following statements.

p: Suman is brilliant.

q: Suman is rich.

r: Suman is honest.

The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as


A

~[q(p~r)]

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B

~qpr

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C

~(pr)q

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D

~p(qr)

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Solution

The correct option is A

~[q(p~r)]


Step 1. Given Statements :

p : Suman is brilliant

q : Suman is rich

r : Suman is honest;

t : “Suman is brilliant and dishonest if and only if Suman is rich”

Step 2. To find ~ t :

t:(p~r)q~t:~[(p~r)q](1)~(pq)=p~qandpq=(pq)(qp)~(pq)=~(pq)~(qp)=(p~q)(q~p)(2)

Step 3. Conclusion from (1) and (2) :

~t:[(p~r)~q][q~(p~r)which is equivalent to ~[q(p~r)].

Hence, the correct option is A.


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