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## Homework Statement

Prove that: A is a subset of B if and only if (A intersection B)=A

## Homework Equations

## The Attempt at a Solution

I tried proving the right side, that is(A [tex]\cap[/tex] B)=A

For two sets to be equal then they have to be subsets of each other...so:

(A [tex]\cap[/tex] B) [tex]\subseteq[/tex] A and A [tex]\subseteq[/tex] (A [tex]\cap[/tex] B)

So if we assume an element x [tex]\in[/tex] (A[tex]\cap[/tex]B), then by definition, x[tex]\in[/tex]A and x [tex]\in[/tex]B. Thus we proved that (A[tex]\cap[/tex]B)[tex]\subseteq[/tex]A.

In not quite sure how to prove the opposite, because if x is an element of A, that doenst necessarily mean that x is an element of A[tex]\cap[/tex]B...so i need help with the rest of it..or if you got any other ideas on how to approach it.

Thank you,

Emira!