Question

Which of the following sets are equal?
(i) $A=\{1,2,3,4\},B=\{4,3,2,1\}$
(ii) $A=\{4,8,12,16\},B=\{8,4,16,18\}$
(iii) $X=\{2,4,6,8\}$
$Y=$ { $x:x$ is a positive even integer $0<x<10$ }
(iv) $P=$ { $x:x$ is a multiple of $10$, $x\in N$ }
$Q=\{10,15,20,25,30,...\}$

Answer 1

$\left(1\right)$ $A=\{1,2,3,4\}$ and $B=\{1,2,3,4\}$

so $A=B$

$\left(2\right)$ $A=\{4,8,12,16\}$ and $B=\{4,8,16,18\}$

so $A\ne B$

$\left(3\right)$ $X=\{2,4,6,8\}$

for $x=$even

and $0<x<10$

$Xϵ\{2,4,6,8\}$

so, $Yϵ\{2,4,6,8\}$

Thus $X=Y$

$\left(4\right)$ $P$ is multiple of $10$ and itis a subset of natural no.

so, $P=\{10,20,30,\mathrm{40....}\}$

and $Q=\{10,15,20,25,....\}$

so $P\ne Q$