Let A be a set with n elements. A relation R on A is called reflexive and symmetric if it is both reflexive and symmetric.
(i) Show that every such relation must contain exactly n ordered pairs of the form (a,a) with a∈A.
(ii) Obtain a general formula for the total number of relations on A that are simultaneously reflexive and symmetric.
(iii) Using your formula, determine the number of reflexive and symmetric relations on a set with 5 elements.