Sets, Relations and Function: Let A=\xinmathbfR:|x+1|<2\ and B=\xinmathbfR:|x-1|ge2\ . Then which… | JEE Main 2022

JEE Main 2022 (Online) 25th June Evening ShiftQuestion 1

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

Sets, Relations and Function

$A-B=(-1,1)$$B-A=\mathbf{R}-(-3,1)$✓ Correct answer$A\cap B=(-3,-1]$$A\cup B=\mathbf{R}-[1,3)$

Solution

$A=(-3,1)$, $B=(-\infty,-1]\cup[3,\infty)$. $A-B=(-1,1)$ true. $A\cap B=(-3,-1]$ true. $A\cup B=\mathbf R-[1,3)$ true. $B-A=(-\infty,-3]\cup[3,\infty)=\mathbf R-(-3,3)\ne\mathbf R-(-3,1)$. So (B) is NOT true: option B.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2022 (Online) 25th June Evening Shift)

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