Consider the following statements: A : Rishi is a judge. B :... | Mathematics | SolveeIt | Solveeit

Today, August 24

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 → (A ∨ C)

B

(~ B) ∧ (A ∧ C)

C

B → ((~ A) ∨ (~ C))

D

B → (A ∧ C)

Answer

(~ B) ∧ (A ∧ C)

Explanation

Solution

The given statement is:

$(A ∧ C) → B$

The negation of the statement is :

$~ {(A ∧ C) → B}$ or $~ {~ (A ∧ C) ∨ B}$

$∴ (A ∧ C) ∧ (~ B)$ or $(~ B) ∧ (A ∧ C)$

Hence, the correct option is (B): (~ B) ∧ (A ∧ C)