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. $\sim (Q\leftrightarrow (P\wedge \sim R\left)\right)$
• B. $\sim Q\leftrightarrow \sim P\wedge R$
• C. $\sim (P\wedge \sim R)\leftrightarrow Q$
• D. $\sim P\wedge (Q\leftrightarrow \sim R)$

Answer 1

The correct option is A $\sim (Q\leftrightarrow (P\wedge \sim R\left)\right)$

Suman is brilliant and dishonest if and only if Suman is rich is expressed as
$Q\leftrightarrow (P\wedge \sim R)$
Negation of it will be $\sim (Q\leftrightarrow (P\wedge \sim R\left)\right)$