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Mathematical Reasoning
medium
Consider the following statements :
$A$ : Rishi is a judge.
$B$ : Rishi is honest.
$C$ : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is
A
$B \rightarrow( A \vee C )$
B
$(\sim B ) \wedge( A \wedge C )$
C
$B \rightarrow((\sim A ) \vee(\sim C ))$
D
$B \rightarrow( A \wedge C )$
(JEE MAIN-2022)
Solution
$\sim(( A \wedge C ) \rightarrow B )$
$\sim(\sim( A \wedge C ) \vee B )$
Using De-Morgan's law
$( A \wedge C ) \wedge(\sim B )$
Standard 11
Mathematics
