If `R` be a relation `<` from `A = {1, 2, 3,4) to B = (1,3,5)` that is `(a, b) in R iff a lt b`, then `R o R^-1` is

Let R={(x,y):x^(2)+y^(2)=1,x,y in R} be a relation in R. Then the relation R is

Let R be a relation in the set of natural numbers N defined by xRy if and only if x+y=18 . Is R an equivalence relation?

Let R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.

Let R be a relation on a set A such that R= R^(-1) . Then R is :

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