Answer:
Since A={a,b}, then [tex]P(A)=\{\emptyset, \{a,b\}, \{a\}, \{b\}\}[/tex]. Remember that the Cartesian Product of two sets A, B is defined by
[tex]A\times B=\{(x,y): x\in A \text{ and } y\in B\}[/tex]. Then
[tex]A\times P(A)=\{(a,\emptyset),(a,\{a,b\}),(a,\{a\}), (a,\{b\}), (b,\emptyset),(b,\{a,b\}),(b,\{a\}), (b,\{b\})\}[/tex]
