Number of Reflexive and irreflexive relation

Define a reflexive relation.

If the numbers of different reflexive relations on a set A is equal to the number of different symmetric relations on set A, then the number of elements in A is

Let set A=(a,b,c), then number of possible reflexive relations on set A are

If a set A has 13 elements and R is a reflexive relation on A with a elementss, n in Z^(+) , then

If a set has 13 elements and R is a reflexive relation on A with n elements, then

Definition of Reflexive relation

If the number of reflexive relations defined on a set A is 64, then the number of elements in A is _____

If R and S are relations on a set A, then prove the following: R and S are symmetric $R nn S and R uu S are symmetric R is reflexive and S is any relation hat varphi R uu S is reflexive.