# Homework Help: Union/Intersection Proof

1. Mar 17, 2012

### Bipolarity

1. The problem statement, all variables and given/known data

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) $f(E \cap F) \subset f(E)\cap f(F)$

2. Relevant equations

3. 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

Last edited: Mar 17, 2012
2. Mar 17, 2012

### Poopsilon

I don't believe b) is true..

3. Mar 17, 2012

### Bipolarity

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

BiP

4. Mar 17, 2012

### Poopsilon

Ok ya 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.

5. Mar 17, 2012

### Bipolarity

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

BiP

6. Mar 17, 2012

### micromass

Yes, because you are supposed to finish it.