Question

If $A^{\prime }\cup B=U$, then show that $A\subset B$

Answer 1

$A^{\prime }\cup B=U$

we have $A^{\prime }\cup B=U^{\prime }$

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

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

It means no elements is common in $A$ & $B$ which would only possible if $A$ & $B$ are disjoint sets hence for that $A\subset B$. It is true.