Let N be the set of all positive integers and R be a relation on N, defined by R = {(a,b): a is a factor of b), show that R is reflexive and transitive.

If N denotes the set of all natural numbers and R be the relation on N xx N defined by (a, b) R (c, d) if ad(b+ c)=bc(a+d) . Show that R is an equivalence relation.

Let A be the set of all points in a plane and R be a relation on A defined as R={(P,Q): distance between P and Q is less than 2 units). Show that R is reflexive and symmetric but not transitive.

If Z is the set of all integers and R is the relation on Z defined as R={(a, b): a, b in Z and a-b is divisible by 3. Prove that R is an equivalence relation.

Let R be the relation on Z defined by aRb iff a-b is an even integer. Show that R is an equivalence relation.

Let A = {1,2,3,4,5,6} and Let R be a relation on A defined by R {(a,b)| a divides b} Find R.

Let A = {1,2,3,4,5,6} and Let R be a relation on A defined by R {(a,b)| a divides b} Find dom R.

Let A = {1,2,3,4,5,6} and Let R be a relation on A defined by R {(a,b)| a divides b} Find rng R.

Let A = {1,2,3,4,5,6} and Let R be a relation on A defined by R {(a,b)| a divides b} Find Dom R^(-1) .

Let a relation R on the set A of real numbers be defined as (a, b) inR implies1+ab >0, AA a, b in A . Show that R is reflexive and symmetric but not transitive.

Let A = {1,2,3,4,5,6} and Let R be a relation on A defined by R {(a,b)| a divides b} Find R^(-1) .