JEE Main 2022 · 24 Jun · Shift 2 · Mathematics Q18

MathematicsSingle correct+4 / -1Question 18 of 90

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

B\rightarrow(A\vee C)

(\sim B)\wedge(A\wedge C)

B\rightarrow((\sim A)\vee(\sim C))

B\rightarrow(A\wedge C)

Answer and worked solution

Official answer: B

The statement is $(A\wedge C)\rightarrow B$ .

Negation. $\sim(p\rightarrow q)\equiv p\wedge\sim q$ , so it is $(A\wedge C)\wedge(\sim B)$ , i.e. $(\sim B)\wedge(A\wedge C)$ .

(B)

Topics:Mathematical reasoning

JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 18