The number of relations on the set A = {1,2,3,4} that are reflexive and symmetric but not transitive is ___

The number of relations that are reflexive and symmetric $=2^{\frac{4^2-4}{2}}=2^6=64$

The number of equivalence relations on the set A $=\text{ 1}+\text{4}+\text{3}+\text{6}+\text{1}=\text{15}$

$\therefore$ No. of relations that are reflexive and symmetric but not transitive
    = 64 - 15 = 49