Question

Show that the four conditions are equivalent
$\begin{array}{cc}& i)A\subset B\\ & ii)A-B=\varphi \\ & iii)A\cup B=B\\ & iv)A\cap B=A\end{array}$

Answer 1

$\because A\subset B$,It means all the elements of $A$ is present in $B$.

$\therefore A-B=\varphi$

$\therefore A\cup B$(because all elements of $A$ are present in $B$)

$A\cap B=B$ [intersection means only we can take common elements of set $A$ & set $B$].