Let A be the non-empty set of children in a family. The relation ‘x is a brother of y’ on A is

Let r denotes the relation ‘x is brother of x’. Let x∈A. If x is a girl, then we cannot say x is brother of x.∴                               (x, x)∉R∴ R is not reflectiveLet                                (x, y) ∈ R∴ x is a brother of y.∴y may or may not be a boy.∴We cannot say that (y, x)  .∴R is not symmetricLet               (x, y) ∈R and (y, z) ∈R∴x is brother of y and y is brother of z.∴x is brother of z⇒ (x, z) ∈R∴R is transitive