Determine the number of binary relations on a set $\displaystyle A = {a_1, a_2, . . . , a_n}$ containing for each

pair of distinct elements $\displaystyle a_i, a_j$

at least one of the ordered pairs $\displaystyle (a_i, a_j)$ and $\displaystyle (a_j , a_i)$ (maybe both)