1. Feb 3, 2004

Caldus

How do I start a problem like this? I need to prove it's true or provide a counterexample if it is false.

A \ (B union C) = (A \ B) union (A \ C)

If someone could point me in the right direction, then I would appreciate it.

2. Feb 4, 2004

phoenixthoth

i would start with a venn diagram. three circles: one for A, one for B, and one for C. then shade in A \ (B union C) and draw a separate diagram and shade in (A \ B) union (A \ C). if the two shaded regions are identical, then try to prove it's true. if they're not identical, that will narrow your search for a counterexample.

3. Feb 4, 2004

matt grime

you could just prove it:

x in A\(BuC) iff (x in A) and (x not in (BuC) iff etc...

Of course we could pass to a universe, X\Y = X intersect Y^c, and the question just needs you to know about interesections.

4. Feb 11, 2004

[ infinite ]

I'm not too familiar with this, but if we take a numeric example, then does 'union' act as the addition operator? Can we perform arithmetic operations on sets?

For example, take A={3}, B={2}, C={5}

Then would

A /(B u C) = 3 / (2+5) = 3/7

whereas

(A/B) u (A/C) = (3/2) + (3/5) = 21/10

thus providing a counterexample?

Please correct me if I'm wrong.

Last edited: Feb 11, 2004
5. Feb 12, 2004

Muzza

Yes, in some sense, but it's hardly defined exactly like the "normal" addition operator... See Wikipedia, set theory for more info.

In your example, B union C = {2, 5}, not 7!

Also, \ stands for complement, not division.

Last edited: Feb 12, 2004