Sets, Relations and Function: If A=\xinmathbfR:|x|<2\ and B=\xinmathbfR:|x-2|ge3\ ; then : | JEE Main 2020

JEE Main 2020 (Online) 9th January Evening ShiftQuestion 1

If $A=\{x\in\mathbf{R}:|x|<2\}$ and $B=\{x\in\mathbf{R}:|x-2|\ge3\}$; then :

Sets, Relations and Function

$A-B=[-1,2)$$B-A=\mathbf{R}-(-2,5)$✓ Correct answer$A\cap B=(-2,-1)$$A\cup B=\mathbf{R}-(2,5)$

Solution

$A=(-2,2)$. $|x-2|\ge3\Rightarrow x\le-1$ or $x\ge5$, so $B=(-\infty,-1]\cup[5,\infty)$. $A\cap B=(-2,-1]$, $A-B=(-1,2)$, $B-A=(-\infty,-2]\cup[5,\infty)=\mathbf R-(-2,5)$, $A\cup B=\mathbf R-[2,5)$. Only (B) is true.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2020 (Online) 9th January Evening Shift)

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