need help with this

This is secretly asking you for a proof, but you may treat it as a writing assignment if that helps you think through the problem better. Let A C X and x an equivalence relation R C X X X. Note (no need to prove this, but you may want to understand this) that RA x A is an equivalence relation on A. We let X / N and A/ N be the resulting quotients. We can endow A with the subspace topology, then induce the quotient topology on A/ N. Call this topology '3'. On the other hand, A/ N can be considered a subset of X / N, so we can endow A/ N with the subspace topology inherited from the quotient topology on X / N. Call this '3". Are '3' and '3" the same topology? Explore, write; explain your thoughts