Question

If $A\subseteq B$ then for any set C, prove that $(C-B)\subseteq (C-A)$

Answer 1

Let $A\subseteq B$ be given.

Let $xϵ(C-B)$. Then,

$xϵ(C-B)\Rightarrow xϵCandx\text{/}ϵB$

$\Rightarrow xϵCandx\text{/}ϵA[\because A\subseteq B]$

$\therefore (C-B)\subseteq (C-A)$

Hence, $A\subseteq B\Rightarrow (C-B)\subseteq (C-A)$