Let N be the set of all natural numbers and R be a relation in N defined by : R = {(a, b) : a is a factor of b} Show that R is reflexive and transitive.

Let S be the set of all real numbers and let R be the relation in S defined by R = {(a,b), a leb^2 }, then

Let N be the set of natural number and R be the relation in NxxN defined by : (a,b) R (c,d) iff ad = bc, for all (a,b), (c,d) in NxxN Show that R is an equivalence relation.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxxNdot

Check whether the relation R in R defined by R = {(a, b) : a le b^3} is reflexive, symmetric or transitive.

Let Z be the set of all integers and R be the relation on Z defined as R = (a,b) : a,b in Z and a-b is divisible by 5) Prove that R is an equivalence relation.

Let N be the set of natural numbers and the relation R be defined on N such that R = {(x, y) : y = 2x, x, y in N} . Is this relation a function ?

Let L be the set of all lines in a plane and R be the relation on L defined as R = (l,m) : l is perpendicular to m). Check whether R is reflexive, symmetric or transitive.

Let A = N xx N being the set of natural numbers. Let '*' be a binary operation on A defined by (a,b) * (c,d) = (a+c,b+d). Show that '*' is associative.

Check whether the relation R in R, defined by R= {(a, b): a le b^3 ) is reflexive, symmetric or transitive ?