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
Select the correct option:
A
$B \rightarrow(A \vee C)$
B
$(\sim B) \wedge(A \wedge C)$
C
$B \rightarrow((\sim A) \vee(\sim C))$
D
$B \rightarrow(A \wedge C)$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$
\begin{aligned}
& \sim((A \wedge C) \rightarrow B) \\
& \sim(\sim(A \wedge C) \vee B)
\end{aligned}
$$
Using De-Morgan's law
$$
(A \wedge C) \wedge(\sim B)
$$
Option B is correct.
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