Question

In the following, state whether $A=B$ or not:
(i) $A=\{a,b,c,d\}B=\{d,c,b,a\}$
(ii) $A=\{4,8,12,16\}B=\{8,4,16,18\}$
(iii) $A=\{2,4,6,8,10\}B=\{x:x\text{is a positive even integer and}x\le 10\}$
(iv) $A=\{x:x\text{is a multiple of 10}\},B=\{10,15,20,25,30,...\}$

Answer 1

(i) $A=\{a,b,c,d\};B=\{d,c,b,a\}$
The order in which the elements of a set are listed is not significant.
$\therefore A=B$
(ii) $A=\{4,8,12,16\};B=\{8,4,16,18\}$
It can be seen that $12ϵA$ but $12\text{/}ϵB$.
$\therefore A\ne B$
(iii) $A=\{2,4,6,8,10\}$
$B=\{x:x\text{is a positive even integer and}x\le 10\}$
$=\{2,4,6,8,10\}$
$\therefore A=B$
(iv) $A=\{x:x\text{is a multiple of 10}\}$
So, $A=\{10,20,30,\mathrm{40....}\}$
$B=\{10,15,20,25,\mathrm{30....}\}$
It can be seen that $15ϵB$ but $15\text{/}ϵA$.
$\therefore A\ne B$