Question

how to prove the following using defined sets

A=B⇔A⊆B and B ⊆ A

Answer 1

If $A=B$

Thus, for all $x\in A\implies x\in B\iff A\subseteq B$ ,Similarly $y\in B \implies y\in A\iff B\subseteq A$

If $A\subseteq B$ and $B\subseteq A$ , thus by definition $A=B$ .