$\begingroup$

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?

$\endgroup$ 1

1 Answer

$\begingroup$

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

$\endgroup$ 2

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy