| 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 any only if suman is rich" can be expressed as |
A) \[\tilde{\ }(P\wedge \tilde{\ }R)\leftrightarrow Q\]
B) \[\tilde{\ }(P\wedge (Q\leftrightarrow \,\tilde{\ }R)\]
C) \[\tilde{\ }(Q\leftrightarrow (P\wedge \tilde{\ }R))\]
D) \[\tilde{\ }Q\leftrightarrow \,\tilde{\ }P\wedge R\]
Correct Answer: C
Solution :
[c] Suman is brilliant and dishonest is \[P\wedge \sim R\] Suman is brilliant and dishonest iff Suman is rich is \[Q\leftrightarrow (P\wedge \sim R)\] Negative of statement is expressed as \[\sim (Q\leftrightarrow (P\wedge \sim R)\]
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