JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q1

← JEE Main 2022 · 25 Jun · Shift 2

MathematicsSingle correct+4 / -1Question 1 of 90

Let $A=\{x\in\mathbb R:|x+1|<2\}$ and $B=\{x\in\mathbb R:|x-1|\ge2\}$ . Then which one of the following statements is NOT true ?

A-B=(-1,1)

B-A=\mathbb R-(-3,1)

A\cap B=(-3,-1]

A\cup B=\mathbb R-[1,3)

Answer and worked solution

Official answer: B

Sets. $A=(-3,1)$ and $B=(-\infty,-1]\cup[3,\infty)$ .

Check. $A-B=(-1,1)$ ✓; $A\cap B=(-3,-1]$ ✓; $A\cup B=\mathbb R-[1,3)$ ✓. But $B-A=(-\infty,-3]\cup[3,\infty)=\mathbb R-(-3,3)$ , not $\mathbb R-(-3,1)$ .

(B)

Topics:Sets and operations Inequalities and modulus

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JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 1