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. $B\to \left(\right(\sim A)\vee (\sim C\left)\right)$
• B. $(\sim B)\wedge (A\wedge C)$
• C. $B\to (A\vee C)$
• D. $B\to (A\wedge C)$

Answer 1

The correct option is B $(\sim B)\wedge (A\wedge C)$

Given statement is
$(A\wedge C)\to B$
Then its negation is given by
$\sim \left(\right(A\wedge C)\to B)$
or $\sim (\sim (A\wedge C)\vee B)$
Using De-Morgan's low, we get
$(A\wedge C)\wedge (\sim B)$