Answer
a) $A$ $X$ $B$ $X$$C$={(a,x,0),(a,x,1),(a,y,0),(a,y,1),(b,x,0),(b,x,1),(b,y,0),(b,y,1),(c,x,0),(c,x,1),(c,y,0),(c,y,1)}
b) $C$ $X$ $B$ $X$$A$={(0,x,a),(0,x,b),(0,x,c),(0,y,a),(0,y,b),(0,y,c),(1,x,a),(1,x,b),(1,x,c),(1,y,a),(1,y,b),(1,y,c)}
c) $C$ $X$ $A$ $X$$B$={(0,a,x),(0,a,y),(0,b,x),(0,b,y),(0,c,x),(0,c,y),(1,a,x),(1,a,y),(1,b,x),(1,b,y),(1,c,x),(1,c,y)}
d) $B$ $X$ $B$ $X$$B$ ={(x,x,x),(x,x,y),(x,y,x),(x,y,y),(y,x,x),(y,x,y),(y,y,x),(y,y,y)}
Work Step by Step
A={a,b,c}
B={x,y}
C={0,1}
a) Using the definition of cartesian product, we know that $A$ $X$ $B$ $X$$C$ are ordered triplets of any combination of the elements in each set (in the same order as the sets in cartesian product).
$A$ $X$ $B$ $X$$C$={(a,x,0),(a,x,1),(a,y,0),(a,y,1),(b,x,0),(b,x,1),(b,y,0),(b,y,1),(c,x,0),(c,x,1),(c,y,0),(c,y,1)}
b) Using the definition of cartesian product, we know that $C$ $X$ $B$ $X$$A$ are ordered triplets of any combination of the elements in each set (in the same order as the sets in cartesian product).
$C$ $X$ $B$ $X$$A$={(0,x,a),(0,x,b),(0,x,c),(0,y,a),(0,y,b),(0,y,c),(1,x,a),(1,x,b),(1,x,c),(1,y,a),(1,y,b),(1,y,c)}
c) Using the definition of cartesian product, we know that $C$ $X$ $A$ $X$$B$ are ordered triplets of any combination of the elements in each set (in the same order as the sets in cartesian product).
$C$ $X$ $A$ $X$$B$={(0,a,x),(0,a,y),(0,b,x),(0,b,y),(0,c,x),(0,c,y),(1,a,x),(1,a,y),(1,b,x),(1,b,y),(1,c,x),(1,c,y)}
d) Using the definition of cartesian product, we know that $B$ $X$ $B$ $X$$B$ are ordered triplets of any combination of the elements in each set (in the same order as the sets in cartesian product).
$B$ $X$ $B$ $X$$B$ ={(x,x,x),(x,x,y),(x,y,x),(x,y,y),(y,x,x),(y,x,y),(y,y,x),(y,y,y)}
