In what order should the sets be multiplied?

Question

Mathematics

Suppose there are two sets A = {1,2,3} and B = {3,4,5}.
How to solve let's say such a problem A x A x B?
Just calculate C = A x A first and then C x B?
Or is there another way?

Answer 1

is the set of ordered triples of numbers, {(1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 2, 3), ...}. the first from A, the second from A, the third from B. solve simply by enumeration. we fix the first number, then the second, the third we sort through - we write out the triples, then we change the second and again we sort through all the options for the third - we write out the triples, and so on.

Answer 2

https://ru.wikipedia.org/wiki/Direct_work
From left to right.

Answer 3

The order is not important.

Just calculate C = A x A first and then C x B?

If you calculate C = A x B and then A x C, the result will be the same.
The main thing is not to count B x A instead of A x B.