Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find
A x B x C
C x B x A
C x A x B
B x B x B

Solution:

A = {a, b, c}, B = {x, y}, and C = {0, 1} are the three given sets.

A x B x C, C x B x A , C x A x B and B x B x B are the cartesian products of sets A, B and C.

A = {a, b, c}, B = {x, y},

and C = {0, 1}.

A x B x C = {(a, x, 0), (a, y, 1), (b, x, 0), (b, y, 1), (c, x, 0), (c, y, 1)}

C x B x A = {(0, x, a), (0, y, b), (0, c), (1, x, a), (1, y, b), (1, c)}

C x A x B = {(0, a, x), (0, b y), (0, c), (1, a, x), (1, b, y), (1,c)}

B x B x B = {(x, x, x), (x, y, y), (y, x, x), (y, y, y)}

The products are not the same because of the order in which they are multiplied

Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find A x B x C, C x B x A, C x A x B, B x B x B

Summary:

A x B x C = {(a, x, 0), (a, y, 1), (b, x, 0), (b, y, 1), (c, x, 0), (c, y, 1)} , C x B x A = {(0, x, a), (0, y, b), (0, c), (1, x, a), (1, y, b), (1, c)}, C x A x B = {(0,a,x), (0,b,y), (0,c), (1,a,x), (1, b, y), (0,c) (1,c)}, B x B x B = {(x, x, x), (x, y, y), (y, x, x), (y, y, y)}