# Nightmares with formal proofs in set theory

1. Mar 26, 2006

### JasonJo

I am having a nightmare trying to prove things in set theory.

One of my homework problems is to prove that:

Dom(R U S) = Dom(R) U Dom(S)

but i have no idea how to really do this. my teacher never went over this stuff!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IT'S SO AGGRAVATING!

can anyone reference a good site or book on how to prove things in set theory, such as the domain, inverse of function only if the function is one-to-one, etc???

ack!

2. Mar 26, 2006

### HallsofIvy

The basic way to prove A is a subset of B is: Let x be a member of A. Then use what ever the definition of A is to show that x also satisfies the definition of B: x is a member of B.

Here, unfortunately, you haven't told us what R and S are and you haven't told us what "Dom" means. If R and S are functions I might guess that "Dom" means domain.

3. Mar 26, 2006

### JasonJo

R and S are relations, Dom means domain

4. Mar 26, 2006

### arildno

Suppose that (x,y) satisfies the relation RUS (i.e, (x,y) is in Dom(RUS)
Then, (x,y) either satisfies the relation R (i.e, (x,y) is in Dom(R)), or (x,y) satisfies the relation S (i.e, (x,y) is in Dom(S))
Thus, Dom(RUS) is contained within Dom(R)UDom(S).

I'll leave to you to show that Dom(R)UDom(S) is contained within Dom(RUS).