Multiplication:
The Cartesian product:
A*B = {(a,b) | a in A, b in B}
B*A = {(b,a) | a in A, b in B}
A bijection from reversing the elements in the pair.
|A*B| = |B*A|
|A|*|B| = |B|*|A|
It is commutative
A*(B*C) = {(a,(b,c)) | a in A, b in B, c in C}
(A*B)*C = {((a,b),c) | a in A, b in B, c...