# Homework Help: Help, proving set theorem

1. Nov 29, 2008

### mbcsantin

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

Prove A contained B iff A n B = A

2. Relevant equations

none

3. The attempt at a solution

I tried to do the questions but im just not sure if i did it right. id appreciate if you can check my work and let me know what changes i have to make. thanks

the symbol "n" means "intersect"
U for Union

(=>) Assume A contained B

Let x is an element of A, since A n A = A, x is an element of A and x is an element of B

Case 1: x is an element of A: Since A contained B, x is an element of B so
x is an element of A n B

Case 2: x is an element of B: If x is an element of B then
x is an element of (A n B)

Hence x is an element of A n B

This shows A contained A n B

(<=) Assume A n B = A then

A’=A’UA
= A’ U (A n B)
=(A’UA) n (A’U B)
= empty set n A’ U B
= A’ U B

Hence
Universe = A’ U B

2. Nov 29, 2008

### e(ho0n3

You don't need the "since A n A = A" part.

You don't need cases here. You want to show that A n B = A: Do this by first showing that A n B is a subset of A and then showing that A is a subset of A n B. (Do you see why this implies A n B = A?)

What is A' exactly? Also, you state that A’=A’UA but then you have that A’=A’UA is the empty set. Surely there is something wrong here. You just need to show that A is a subset of B. Do this by picking a random member of A and show that it also belongs to B.