Practicing Cartesian Products: B x (C x A)

[nicnicman]

Hi, everyone. I'm practicing Cartesian products and wanted to see if I was doing this correctly. Here's the problem

Let A = {x, y, z}, B = {a, b}, C = {1, 3},
Find B x (C x A) (the x denotes multiplication)

Now wouldn't B x (C x A) = B x C x A?

Then we would have:
B x (C x A) = B x C x A = {(a, 1, x), (a, 1, y), (a, 1, z), (a, 2, x), (a, 2, y), (a, 2, z),
(b, 1, x), (b, 1, y), (b, 1, z), (b, 2, x), (b, 2, y), (b, 2, z)}

Is this right?

 

[micromass]

Hi, everyone. I'm practicing Cartesian products and wanted to see if I was doing this correctly. Here's the problem

Let A = {x, y, z}, B = {a, b}, C = {1, 3},
Find B x (C x A) (the x denotes multiplication)

Now wouldn't B x (C x A) = B x C x A?

No, those two aren't equal. We often do identify them, but strictly spoken, they are not equal.

 

[nicnicman]

Yeah, you're right. After a little more looking I found that I was wrong.

Anyway, here is a second crack at it:

B x (C x A) =
{(a, (1, x)), (a, (1, y)), (a, (1, z)), (a, (3, x)), (a, (3, y)), (a, (3, z))
(b, (1, x)), (b, (1, y)), (b, (1, z)), (b, (3, x)), (b, (3, y)), (b, (3, z))}

How's this?

 

[micromass]

That's right!

 

[nicnicman]

Thanks!