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

We are given the statements: $$A$$: Rishi is a judge, $$B$$: Rishi is honest, and $$C$$: Rishi is not arrogant.

The statement "if Rishi is a judge and he is not arrogant, then he is honest" can be written as: $$(A \wedge C) \to B$$

Recall that the negation of an implication $$p \to q$$ is $$p \wedge (\sim q)$$, so $$\sim[(A \wedge C) \to B] = (A \wedge C) \wedge (\sim B)$$.

This can be rewritten as: $$(\sim B) \wedge (A \wedge C)$$

Therefore, the negation is Option B: $$(\sim B) \wedge (A \wedge C)$$.