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This is my first time posting on this form, however I think I have what is a simple question.

In my Linear Algebra homework assignment my professor has asked me to prove $f(A\cap B)\subset f(A)\cap f(B)$ where $A,B \subset X$ where $f$ is a function that maps $X$ to $Y$.

Now I don't necessarily have a question about that problem just yet, but he asks us if the opposite inclusion is true as well. However, I have no idea what opposite inclusion is, and didn't have any luck finding it on a Google search. Can someone please define that term for me?

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If Martin's answer suited your needs, you can accept it by clicking the checkmark. –  Mark S. Feb 16 at 3:42

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By "the opposite inclusion" your prof means $$ f(A)\cap f(B)\subset f(A\cap B). $$

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Wow thanks for the hasty response that helped out a ton! Have a great day! –  Valentino Feb 8 at 19:51
    
You are welcome! –  Martin Argerami Feb 8 at 21:21

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