How to Correct an Incorrect Proof Involving Set Theory?

[ash25]

Homework Statement

PLEASE HELP!How would you correct this incorrect proof:
Suppose that S∩T≠0,T∩W≠0,and for a contradiction S∩W=0.From the first 2,we have some t∈S∩T,and similarly t∈T∩W.But then t∈S,t∈T,and t∈W.So t∈S∩W,giving a contradiction.

 

[micromass]

There is no way to correct this "proof", since what you're trying to show is false!

Take $$S=[0,3],~T=[1,5],~W=[4,10]$$. Then $$S\cap W=\emptyset$$...

 

[ash25]

Thank you, so the claim was true though, right? It was:
For any sets S,T,and W,if S∩T≠0 and T∩W≠0,then S∩W≠0

 

[micromass]

No, I just gave you a counterexample...

 

[ash25]

You are being so helpful thank you!
but you are saying that the claim is false?

 

[micromass]

but you are saying that the claim is false?

Yes!