Prove that a relation `R` on a set `A` is symmetric iff `R=R^(-1)` .

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

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

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?

Prove that the relation R in set A = {1, 2, 3, 4, 5} given by R = {(a,b): |a-b| is even} is an equivalence relation .

Prove that the relation R in set A = {1, 2, 3, 4, 5} given by R = {(a,b): |a-b| is even} is an equivalence relation .

If R is a symmetric relation on a set A , then write a relation between R and R^(-1) .

If R is a symmetric relation on a set A, then write a relation between R and R^(-1) .