Answer to Question #316057 in Discrete Mathematics for Alamanda

Question

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

Find

a)   A X B X C

b)   C X B X A

c)   B X C X C 

Answer 1

$a:A\times B\times C=\left\{ \left( c,x,0 \right) ,\left( c,x,1 \right) ,\left( c,y,0 \right) ,\left( c,y,1 \right) ,\left( n,x,0 \right) ,\left( n,x,1 \right) ,\left( n,y,0 \right) ,\left( n,y,1 \right) ,\left( b,x,0 \right) ,\left( b,x,1 \right) ,\left( b,y,0 \right) ,\left( b,y,1 \right) \right\} \\b:C\times B\times A=\left\{ \left( 0,x,c \right) ,\left( 0,x,n \right) ,\left( 0,x,b \right) ,\left( 0,y,c \right) ,\left( 0,y,n \right) ,\left( 0,y,b \right) ,\left( 1,x,c \right) ,\left( 1,x,n \right) ,\left( 1,x,b \right) ,\left( 1,y,c \right) ,\left( 1,y,n \right) ,\left( 1,y,b \right) \right\} \\c:B\times C\times C=\left\{ \left( x,0,0 \right) ,\left( x,0,1 \right) ,\left( x,1,0 \right) ,\left( x,1,1 \right) ,\left( y,0,0 \right) ,\left( y,0,1 \right) ,\left( y,1,0 \right) ,\left( y,1,1 \right) \right\}$