# Homework Help: Proving set theorems

1. Mar 2, 2009

### j9mom

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

I am very confused on how to prove these set theories. The statements seem to prove themselves just by the definitions of the symbols. For example:

If A is contained or equal to B union C and A intersect B = {} (the empty set) then A is contained or equal to C.

3. The attempt at a solution
What I have is:

Assume that A is contained in or equal to B union C. So, any element X that is in A will also be in either B or C. However, we also assume that A n B is the empty set, there is not element in B that is in A. Hence, any X must be contained in C. Therefore A is contained in or equal to C.

This seems too easy... What am I assuming that i need to prove?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 2, 2009

### Dick

It may seem too easy. But that is pretty much the whole proof. Well done. Easy theorems deserve easy proofs.

3. Mar 2, 2009

### j9mom

THANKS, that give me confidence!

4. Mar 3, 2009

### HallsofIvy

Generally, speaking, for sets, A, B, you prove "A = B" by proving "A is a subset of B" and "B is a subset of A".

And you prove "A is a subset of B" by starting "if x is in A" and using the definitions of A and B to conclude "x is in B".