## Main Question or Discussion Point

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.

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
Homework Helper
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.

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.

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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 for more info.

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

Also, \ stands for complement, not division.

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