The number of relations, defined on the set a , b , c , d , which are both reflexive and symmetric, is equal to:

Step-by-step solution

For a set with n = 4 elements, reflexive condition requires all diagonal pairs (a,a), (b,b), (c,c), (d,d) to be included. For symmetric relations, non-diagonal pairs come in symmetric pairs. Number of such pairs = 4 2 = 6 . For each pair, we either include both elements or exclude both → 2 choices each. Total reflexive and symmetric relations = 2^6 = 64 .