Don't know where to start with this one...

[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.

[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.

[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.

[[ 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.

[Muzza]

does 'union' act as the addition operator?


Yes, in some sense, but it's hardly defined exactly like the "normal" addition operator... See Wikipedia, set theory (http://en.wikipedia.org/wiki/Naive_set_theory) for more info.

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

Also, \ stands for complement, not division.