#Question regarding subsets A,B and proof ๐‘“(๐ดโˆฉ๐ต) subset of ๐‘“(๐ด)โˆฉ๐‘“(๐ต)

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leaden roost
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I have a question that says:
let f: X -> Y and A is a subset of X and B is a subset of Y.
Prove that ๐‘“(๐ดโˆฉ๐ต) is a subset of ๐‘“(๐ด)โˆฉ๐‘“(๐ต)...
I have seen the proof where A,B are both subsets of X... But ive never seen any where B is a subset of Y and I do not really know what that means either ... Is it still the same proof as where A,B are both subsets of X? If not what is the difference....
Thank you for your time... Im just really confused about B ...

analog questBOT
leaden roost
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I guess since its the intersection then it doesnt really matter? because u are still taking the set with values both in X and Y ?