Prove or find counterexamples

[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!

 

[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)) ?

 

[mbcsantin]

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

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)

 

[daveyinaz]

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

 

[HallsofIvy]

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)

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!