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Mathematical Reasoning
hard
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 equivalently expressed as
A
$ \sim Q \leftrightarrow \, \sim P \vee R$
B
$ \sim Q \leftrightarrow \, \sim P \wedge R$
C
$ \sim Q \leftrightarrow P\, \vee \sim R$
D
$ \sim Q \leftrightarrow P\, \wedge \sim R$
(JEE MAIN-2015)
Solution
Suman is brilliant and dishonest can be experessed as $P \wedge \sim R$
therefore given statement is equal to $\left( {P \wedge \sim R} \right) \leftrightarrow Q$
Negation of the above statement is
$ \sim Q \leftrightarrow P \wedge \sim R$
Standard 11
Mathematics
