Can a relation R on a set A be both symmetric and antisymmetric?

Let A ={1,2,3} be a given set. Define a relation on A which is symmetric but not antisymmetric on A

When is a relation R on a set A not antisymmetric? Let A={1,2,3,4} and R be a relation on A defined by R={(1,1), (2,2), (3,4), (3,3),(2,1), (4,3)}. Is R antisymmetric on A?

Prove that a relation R on a set A is symmetric iff R=R^-1

When is a relation R on a set A not symmetric ? Let X= {1,2,3,4} and R be a relation on set X defined by R ={(1,2), (3,4), (2,2), (4,3), (2,3) }. Is R symmetric on X?

If number of relations defined on set A those are reflexive and symmetric is 1024 then number of relations those are neither symmetric nor reflexive on set A is

Consider the set A = {a, b, c}. Give an example of a relation R on A. which is : Symmetric and transitive but not reflexive.

If R is a relation on a set A, prove that R is symmetric iff R^-1 = R.

Let R and S be two relations on a set A. If (i) R and S are both symmetric on A prove that R cup S and R cup S are also symmetric on A

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