Show that the relation R on the set A of real numbers defined as R = {(a,b): a `lt=b`).is reflexive. and transitive but not symmetric.

Show that the relation R in the set of real numbers, defined as R = {(a,b): a le b^(2) } is neither reflexive nor symmetric nor transitive.

Check if the relation R on set of real numbers, defined as R = {(a,b) : aleb^3} is reflexsive, symmetric or transitive.

Show that the relation R defined on the set Z of all integers defined as R={(x,y):x-y is an integer} is reflexive, symmertric and transtive.

Give an example of a relation which is reflexive, transitive but not symmetric.

Show that the relation R on the set Z of integers given by R = {(a,b): 2 divides (a - b)} is an equivalence relation.

Given an example of a relation which is reflexive, transitive but not symmetric.

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.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.