Proving Set Theory Problem: Counterexample for (A-B)intersect(A-C)=empty set

[physicsgirlie26]

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!

 

[ircdan]

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!

that doesn't quite work, to show

If (A-B)intersect(A-C)=empty set, then B intersect C = empty set is a false statement, you need to find A, B, C such that (A-B)intersect(A-C)=empty set but B intersect C != empty set

 

[physicsgirlie26]

Ok how about this:

Proof:

Let A={4,26}, B={4,23}, and C={26,23}. If (A-C)=26 and (A-C)=4, that means that (A-B)intersect(A-C) equals the empty set. But B intersect C = 23 which is not the empty set, therefore there is a contradiction.

How is that?

 

[ircdan]

Ok how about this:

Proof:

Let A={4,26}, B={4,23}, and C={26,23}. If (A-C)=26 and (A-C)=4, that means that (A-B)intersect(A-C) equals the empty set. But B intersect C = 23 which is not the empty set, therefore there is a contradiction.

How is that?

good work :)

(I think you mean A-B = {26} though)

 

[physicsgirlie26]

haha got it!


Thank you!