# Math Help - Cartesian products of Sets

1. ## Cartesian products of Sets

For A={ the empty set , {the empty set}}. Determine A X P(A)

2. Originally Posted by nikie1o2
For A={ the empty set , {the empty set}}. Determine A X P(A)
$A = \{\emptyset, \{\emptyset\}\}$

$P(A)$ is the set of all subsets. Find this first:

$P(A) = \{A, \emptyset, \{\{\emptyset\}\}, \{\emptyset\}\} = \{\{\emptyset, \{\emptyset\}\}, \emptyset, \{\{\emptyset\}\}, \{\emptyset\}\}$

Then $A \times P(A)$ is a set of all combinations of ordered pairs $(x,y)$ such that $x \in A$ and $y \in P(A)$