Question

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

Answer 1

Answer:

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

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

$A\times P(A)=\{(a,\emptyset),(a,\{a,b\}),(a,\{a\}), (a,\{b\}), (b,\emptyset),(b,\{a,b\}),(b,\{a\}), (b,\{b\})\}$