Let R be a relation on a set A = {a_1, ..., a_n} of size n. Let M_R be the 0-1 matrix representing R (i.e., the entry m_ij = 1 if (a_i, a_j) elementof B and zero otherwise). (a) How many unique relations are there on A (in terms of n)? (b) The complement relation is defined as R = {(a, b)|(a, b) NotElement R} Say that the number of nonzero entries in M_R (that is, the number of 1 s) is k. How many entries are there in M_R? Briefly justify your answer. (c) How many reflexive relations are there on a set of size n? Briefly justify- your answer. (d) How many symmetric relations are there on a set of size n? Briefly justify- your