Question

Let A = {m, n, o}, B = {a, b}, and C = {7, 2}. Find: a) A x B x C. b) C x B x A. c) C x A x B. d) B x B x B.

Answer 1

Let $A = \{m, n, o\}, B = \{a, b\},$ and $C = \{7, 2\}.$

Let us find the following direct products:

a) $A \times B \times C=\{(m,a,7),(m,a,2),(m,b,7),(m,b,2),(n,a,7),(n,a,2),(n,b,7),(n,b,2), \\(o,a,7),(o,a,2),(o,b,7),(o,b,2)\}$

b)

$C \times B \times A=\{(7,a,m),(7,a,n),(7,a,o),(7,b,m),(7,b,n),(7,b,o), (2,a,m),(2,a,n), \\(2,a,o),(2,b,m),(2,b,n),(2,b,o)\}$

c) $C \times A \times B=\{(7,m,a),(7,m,b),(7,n,a),(7,n,b),(7,o,a),(7,o,b), (2,m,a),(2,m,b),\\(2,n,a),(2,n,b),(2,o,a),(2,o,b)\}$

d) $B \times B \times B=\{(a,a,a),(a,a,b),(a,b,a),(a,b,b),(b,a,a),(b,a,b),(b,b,a),(b,b,b)\}.$