MathDB

Let

N

be the number of ordered pairs of nonempty sets

\mathcal{A}

and

\mathcal{B}

that have the following properties: • \mathcal{A} \cup \mathcal{B} \equal{} \{1,2,3,4,5,6,7,8,9,10,11,12\}, • \mathcal{A} \cap \mathcal{B} \equal{} \emptyset, • The number of elements of

\mathcal{A}

is not an element of

\mathcal{A}

, • The number of elements of

\mathcal{B}

is not an element of

\mathcal{B}

. Find

N

Problem Statement