Question

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. $B \rightarrow( A \wedge C )$

Answer 1

Answer: (B)

$\sim(( A \wedge C ) \rightarrow B )$
$\sim(\sim( A \wedge C ) \vee B )$
Using De-Morgan's law
$( A \wedge C ) \wedge(\sim B )$