Answer
a) $A \times B=\{(a,y), (a,z), (b,y), (b,z), (c,y), (c,z), (d,y), (d,z) \}$.
b) $B\times A=\{(y, a), (y, b), (y,c), (y,d), (z, a), (z, b), (z,c), (z,d)\}$.
Work Step by Step
a)
$A\times B=\{(a,b): a\in A$ and $b\in B\}$.
In words, $A \times B$ is a set of ordered pairs, where the first coordinate of each ordered pair comes from $A$, the second coordinate of each ordered pair comes from $B$, and each element of $A$ is paired with each element of $B$.
So $A \times B=\{(a,y), (a,z), (b,y), (b,z), (c,y), (c,z), (d,y), (d,z) \}$.
b)
$B\times A=\{(b,a): b \in B$ and $a \in A \}$
In words, $B \times A$ is a set of ordered pairs, where the first coordinate of each ordered pair comes from $B$, the second coordinate of each ordered pair comes from $A$, and each element of $B$ is paired with each element of $A$.
Thus $B\times A=\{(y, a), (y, b), (y,c), (y,d), (z, a), (z, b), (z,c), (z,d)\}$.
