1. ## Set theory help please!

I was wondering if someone could please look over my proof of this set theory problem and let me know if I am doing it right or not and give me some help.

Provide a counterexample for the following:

If (A-B)intersect(A-C)=empty set, then B intersect C = empty set.

Proof:

Assume that (A-B)intersect(A-C) does not equal the empty set. Let A={4,26}, B={4,23}, and C={26,23}. Since (A-C)=26 and (A-C)=4, that means that (A-B)intersect(A-C) does not equal the empty set. So B intersect C equals 23 which is also not the empty set.

Thank you for your help!

2. Originally Posted by calcprincess88
Provide a counterexample for the following:
If (A-B)intersect(A-C)=empty set, then B intersect C = empty set.
Proof:
Assume
You are not doing a proof, you are giving a counterexample to show that the statement is false.
This is the way it is done. Find a specific example such as: A={1,2,3}, B={1,2} & C={2,3}.
Now show that those sets satisfy the hypothesis (the if part) but fail to satisfy the conclusion (the then part). Do not assume anything beyond the example you choose..