## Discrete Mathematics with Applications 4th Edition

a. $A\times B=\{(w,a), (w,b), (x,a), (x,b), (y,a), (y,b), (z,a), (z,b)\}$. This set contains 8 elements. b. $B\times A=\{(a,w), (a,x), (a,y), (a,z), (b,w), (b,x), (b,y), (b,z)\}$. This set contains 8 elements. c. $A\times A=\{(w,w), (w,x), (w,y), (w,z), (x,w), (x,x), (x,y), (x,z), (y,w), (y,x), (y,y), (y,z), (z,w), (z,x), (z,y), (z,z)\}$. This set contains 16 elements. d. $B\times B=\{(a,a), (a,b), (b,a), (b,b)\}$. This set contains 4 elements.
The number of elements in a Cartesian product is equal to the product of the number of elements in each set. Note that the order of the elements in the Cartesian product is irrelevant, but the order of the elements in the ordered pairs within the Cartesian product is relevant (e.g., $(1,2)\ne(2,1)$).