MathDB

Let

S_1, S_2, \dots, S_{2^n - 1}

be the nonempty subsets of

\{1, 2, \dots, n\}

in some order, and let

M

be the

(2^n - 1) \times (2^n - 1)

matrix whose

(i, j)

entry is

m_{ij} = \left\{ \begin{array}{cl} 0 & \text{if $S_i \cap S_j = \emptyset$}, \\ 1 & \text{otherwise}. \end{array} \right.

Calculate the determinant of

M

A2