Question

If $A\cap B^{\prime }=\varphi$, then show that $A=A\cap B$ and hence show that $A⊑B$.

Answer 1

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

Then show that $A=A\cap B$ and Show that $A\subseteq B$

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

Let, $x\in A\because x\notin B^{\prime }$

$\Rightarrow x\in (B^{\prime }{)}^{\prime }$

$x\in B$

$A\subseteq B$ $\because A=A\cap B$