jee-main 2011 Q71

jee-main · India Not Maths
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
(1) $\sim(\mathrm{Q}\leftrightarrow(\mathrm{P}\wedge\sim\mathrm{R}))$
(2) $\sim Q\leftrightarrow\sim P\wedge R$
(3) $\sim(P\wedge\sim R)\leftrightarrow Q$
(4) $\sim P\wedge(Q\leftrightarrow\sim R)$
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\\
(1) $\sim(\mathrm{Q}\leftrightarrow(\mathrm{P}\wedge\sim\mathrm{R}))$\\
(2) $\sim Q\leftrightarrow\sim P\wedge R$\\
(3) $\sim(P\wedge\sim R)\leftrightarrow Q$\\
(4) $\sim P\wedge(Q\leftrightarrow\sim R)$