Question

Given, $A=\left\{x:-2<x\le 5,x\in R\right\}$ and $\left\{x:-5\le x<3,x\in R\right\}$

$U=\{x:-5\le x\le 5\}$
i) $A\cap B$
ii) $A^{\prime }\cap B$ on different number lines.

Answer 1

Given that ,

$A=\{x:-2<x\le 5,x\in R\}$

$B=\{x:-5\le x<3\}$

Now ,

$U=\{x:-5\le x\le 5\}$

$A\cap B=\{-5\}$

$A^{{}^{\prime }}$ =$U-A$

$=\{x:-5\le x\le 5,x\in R\}-\{x:-2<x\le 5,x\in R\}$

$=\{x:-5\le x<3\}$

$=B$

Hence ,

$A^{{}^{\prime }}\cap B=$$\{x:-5\le x<3\}\cap$$\{x:-5\le x<3\}$

=$B\cap B$

=B

Hence, this is the answer.