# Determine the number of binary relations on a set A = {a_1, a_2, . . . , a_n}

Determine the number of binary relations on a set $A = {a_1, a_2, . . . , a_n}$ containing for each
pair of distinct elements $a_i, a_j$
at least one of the ordered pairs $(a_i, a_j)$ and $(a_j , a_i)$ (maybe both)