Question

Consider the following statements
$P:$Suman is brilliant
$Q:$Suman is rich
$R:$Suman is honest.
The negative 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. $\sim Q\leftrightarrow P\wedge R$
• 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 $\Rightarrow P\wedge \sim R$

Suman is brilliant and dishonest if and only if suman is rich $\Rightarrow Q\leftrightarrow (P\wedge \sim R)$

Negative of the above statement will be-

$\sim [Q\leftrightarrow (P\wedge \sim R)]$