# A Proof for a Conditional Statement

• Apr 11th 2010, 12:02 PM
loutja35
A Proof for a Conditional Statement
Use the element method for proving a set equals the empty set. Assume that all sets are subsets of a universal set U.

1.) For all sets A and B, if B subset of A compliment then A intersection B = the empty set.

2.) For all sets A, B, and C, if B subset C and A intersection C = the empty set then A intersection B = the empty set.
• Apr 11th 2010, 12:34 PM
Plato
Quote:

Originally Posted by loutja35
Use the element method for proving a set equals the empty set. Assume that all sets are subsets of a universal set U.

1.) For all sets A and B, if B subset of A compliment then A intersection B = the empty set.

2.) For all sets A, B, and C, if B subset C and A intersection C = the empty set then A intersection B = the empty set.

Here is what is expected using the element method.
If $x\in B$ then because $B\subseteq A^c$ then $x \notin A$.
Hence $x\notin A\cap B$ or $A\cap B=\emptyset.$

You try the next one.
• Apr 11th 2010, 12:38 PM
loutja35
I'm sorry, I still don't understand the proof behind this. Could you further explain?
• Apr 11th 2010, 12:45 PM
Plato
Quote:

Originally Posted by loutja35
I'm sorry, I still don't understand the proof behind this. Could you further explain?

First what exactly is meant by the element method?
I assumed it was the same an pick-a-point?

I personally think that this is best done by contradiction.