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

Answer 1

Answer: (B)

$-(Q\leftrightarrow (P\wedge -R\left)\right)$

Let $Q$ be Suman is rich, $P$ be Suman is brilliant and $R$ be Suman is dishonest
Suman is brilliant and dishonest if and only if Suman is rich is expressed as
$Q\leftrightarrow (P\wedge -R)$
Negation of it will $be-(Q\leftrightarrow (P\wedge -R\left)\right)$
Hence, option 'B' is correct.