Question

Let X = {1,2}, Y = {a}, and Z = {α,β}. What is Y × X × Y × Z = ?

Answer 1

What's the order of the product? Are we assuming left to right, like this?
\[\bigg(\big(Y\times X\big)\times Y\bigg)\times Z\]

Answer 2

Dude I don't know. That's how the question is presented to me. I was hoping someone here might know how it's to be interpreted and solved; I was really hoping it's implied. If not I don't know how anyone is supposed to solve this crap because that's how it's given. We didn't go over this in class, and my textbook hasn't arrived yet.

Answer 3

Someone else said but then I guess deleted his comment so I don't know if he was just GUESSING which is not what I need at all -- is it not ((Y × X) × (Y × Z)); and I do not know if it is or isn't that. I was just trying to find that out but googling "cartesian product of multiple sets" or "3" or "4 sets" isn't giving me any hints.

Answer 4

...and even so, then I don't know what that would be; {(a,1), (a,2)} × {(a,α), (a,β)} = ??? what is that even? {((a,1)(a,alpha)),((a,1)(a,beta)),((a,2)(a,alpha)),((a,2)(a,beta))}????

Please someone familiar with discrete math / elementary set theory who is not questioning the problem who understands the problem please explain to me how it is to be solved.

Answer 5

I dont see why it matters...we just want all possible combinations

\(Y \times X \times Y \times Z = \{(a,1,a,\alpha),(a,1,a,\beta),(a,2,a,\alpha), (a,2,a,\beta)\}\)

Answer 6

@calyne make sense?

Answer 7

The Cartesian product is non-associative, which brought up my concern. I think as it's written, you can assume left-to-right order of operations.

Answer 8

I guess I thought these were all real numbers. I agree with left to right would be what this notation means in arbitrary sets.