Question

If $A=\{x\in R:|x|<2\}$and $B=\{x\in R:|x-2|\ge 3\}$ then

• A. $A–B=[-1,2]$
• B. $B–A=R-(-2,5)$
• C. $A\cup B=R-(2,5)$
• D. $A\cap B=(-2,-1)$

Answer 1

The correct option is B

$B–A=R-(-2,5)$

Finding the value:

Given,

$$\begin{gathered} \Rightarrow A=x:x\in (-2,2) \\ \Rightarrow B=x:x\in (\infty ,-1]\cup [5,\infty ) \\ \Rightarrow A\cap B=x:x\in (-2,-1] \\ \Rightarrow B–A=x:x\in (\infty ,-2]\cup [5,\infty ) \\ \Rightarrow A–B=x:x\in (-1,2) \\ \Rightarrow A\cup B=x:x\in (\infty ,2]\cup [5,\infty ) \end{gathered}$$

On comparing 4 options only Option-B is satisfied

Hence, Option (B) is correct.