Question

Given, $A=\{x:-1<x\le -5,x\in R\}$ and $B=\{x:-4<x\le 3,x\in R\}$
Represent on different number lines:
(i) $A\cap B$
(ii) $A^{\prime }\cap B$
(iii) $A-B$

Answer 1

$A=\{x:-1<x\le 5,x\in R\}$

$B=\{x:-4<x\le 3,x\in R\}$

$\left(i\right)$ $A\cap B$=the numbers which are both in A and B

$⟹A\cap B=\{x:-1<x\le 3,x\in R\}$

$\left(ii\right)$ $A^{\prime }\cap B$=the numbers which are not in A but are in B

$⟹A^{\prime }\cap B=\{x:-4<x\le -1,x\in R\}$

$\left(iii\right)$ $A-B=$ the numbers which is in A but not in B

$⟹A-B\{x:3<x\le 5,x\in R\}$