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## Homework Statement

Define f:S→T, where B[itex]\subseteq[/itex]T. Let f

^{-1}(B)={x[itex]\in[/itex]S:f(x)[itex]\in[/itex]B} be the preimage of B.

Demonstrate that for any such map f, f(f

^{-1}(B))=B.

My main question is, would I prove this using set inclusion both ways?

I was going to begin by letting an element be in the preimage of B, and explain what that means, then mapping that element to B. Would this be correct?

I just need a push in the right direction.

Thank you.