Question

For A = {a,b}, determine A x P(A).

Answer 1

Since A={a,b}, then
`P(A)=\{\emptyset, \{a,b\}, \{a\}, \{b\}\}`. Remember that the Cartesian Product of two sets A, B is defined by

`A* B=\{(x,y): x\in A \text{ and } y\in B\}`. Then

`A* P(A)=\{(a,\emptyset),(a,\{a,b\}),(a,\{a\}), (a,\{b\}), (b,\emptyset),(b,\{a,b\}),(b,\{a\}), (b,\{b\})\}`