Proving Subset Inclusion for Intersection of Function Images

[Bipolarity]

Homework Statement

Suppose f: A → B and that E,F are subsets of A.
Prove the following:
a) $f(E \cup F) \equiv f(E) \cup f(F)$
b) $f(E \cap F) \subset f(E)\cap f(F)$

Homework Equations

The Attempt at a Solution

So far I have solved the first one, but I am having trouble with the second. I have no idea where to begin.

BiP

 

[Poopsilon]

I don't believe b) is true..

 

[Bipolarity]

Woops! Sorry I wrote it wrong. I'll change that.

BiP

 

[Poopsilon]

Ok you that should just be a straight element proof then, just follow your nose, if b is in f(E∩F) then there exists an a in E∩F such f(a)=b, if a is in E∩F then a is in E and F.. and so on and so forth.

 

[Bipolarity]

What does "and so on and so forth" supposed to mean? I don't understand your proof sorry. It's incomplete.

BiP

 

[micromass]

It's incomplete.

Yes, because you are supposed to finish it.