Can an Injection Prove Equality in the Intersection of Subsets in a Function?

[ragnes]

f: A-->B is a function. A,B are sets.
Let A1, A2 be contained in/equal to A.

f(A1 intersection A2) is contained in OR equal to f(A1) intersection with f(A2). Show that the equality holds if f is an injection.

I know how to prove that it is contained, but not the equal/injection part. Help please!

 

[╔(σ_σ)╝]

f: A-->B is a function. A,B are sets.
Let A1, A2 be contained in/equal to A.

f(A1 intersection A2) is contained in OR equal to f(A1) intersection with f(A2). Show that the equality holds if f is an injection.

I know how to prove that it is contained, but not the equal/injection part. Help please!

Okay, so far you have proved that...
$$f(A_{1}\cap A_{2}) \subseteq f(A_{1})\cap f( A_{2})$$

When you want to prove equality of sets ( say A and B) you have to show $$A\subset$$ B and $$B \subset A$$.

Where in the process of showing equality are you stuck ?