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

Feb 2011
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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)