# Homework Help: Set Theory Proof Help Needed!

1. Dec 12, 2013

### dainty77

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

Hey guys!

I am new to this forum but saw the helpful posts on set theory proofs and wondered if I could finally get some help with this problem:

Suppose A, B, C, and D are sets with A⊆C and B⊆D. If A∩B=Ø then C∩D=Ø.

This is a biconditional so I have to prove it both ways correct?

Any help would be greatly appreciated!

2. Relevant equations

3. The attempt at a solution

2. Dec 12, 2013

### D H

Staff Emeritus
Where's the biconditional? I only see an if then, not an if and only if. What work have you done?

As stated, the conjecture is false. Are you sure you have the sense correct in terms of which sets are subsets of some other set?

3. Dec 12, 2013

### dainty77

My mistake, it is an "if then" statement.

4. Dec 12, 2013

### D H

Staff Emeritus
As I previously said, the conjecture as written is false. For example, consider sets of fruits. Let A={apple}, B={banana}, C={apple, orange}, and D={banana, orange}. With this, A⊆C, B⊆D, and A∩B=Ø, but C∩D={orange}, which is not the null set.

5. Dec 12, 2013

### dainty77

Wow, the example of using fruit really helped clarify it a lot more. Thank you so much!