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

Given:

A={a, b, c}

B={x, y}

C={0,1}

a) Using the definition of the Cartesian product, we know that $A×B×C$ are ordered triplets of any combination of the elements in each set (in the same order as the sets in the Cartesian product).

$A×B×C$ = {(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 the Cartesian product, we know that $A×B×C$ are ordered triplets of any combination of the elements in each set (in the same order as the sets in the Cartesian product).

$C×(B×A)=$ {(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)}