Question

For any two sets of A and B, prove that
$B^{\prime }\subset A^{\prime }$ if $A\subset B$

Answer 1

$A\subset B\iff A\cup B=B$

$\Rightarrow (A\cup B{)}^{\prime }=B^{\prime }$

USING DEMORGAN'S LAW

$\Rightarrow A^{\prime }\cap B^{\prime }=B^{\prime }$

$\iff B^{\prime }\subset A^{\prime }$

Hence proved.