Prove or find counterexamples

1. Dec 1, 2008

mbcsantin

..using only the definition of the binary product:

for any sets A, B, C in a universe U:

(A x B) x C = A x (B x C)

I have no clue how to even get started with this one. Somebody help me please!!

2. Dec 1, 2008

daveyinaz

Typically you would want to show that both inclusions are true....but in this case.....is the element $$((a,b),c) = (a,(b,c))$$ ?

3. Dec 1, 2008

mbcsantin

Yes, they're equal. It's called the Associative Property of Multiplication.

The property which states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping:
(a . b) . c = a . (b . c)

4. Dec 1, 2008

daveyinaz

I'm sorry..I didn't read the your post correctly if that's the case..was thinking cartesian product.

5. Dec 2, 2008

HallsofIvy

Staff Emeritus
Then please go back and ask whatever question you are REALLY asking. In your original post, A, B, and C are sets. Now you are telling us that they are real numbers. Also in your first post you asked about proving "A x(B x C)= (A x B)x C" but now you are saying that is the "Associative Property of Multiplication" which apparently you are accepting as true. At this point, I have no idea what your question really is!