Each of the following defines a relation R in N.
x R y if xy is square of an integer, x y `in` N. Determine in each ase, whetehr R is reflexive, symetric or transitive.

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

Check whether relation R = {(x, y): x le y^2, x, y in R} , defined on set of real numbers R, is reflexive, symmetric and transitive.

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

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

The given relation is defined on the set of real numbers. a R b iff |a| = |b| . Find whether these relations are reflexive, symmetric or transitive.

Let A be the set of human beings living in a town at a particular time and R be the relation on A defined by R = (x,y) : x is exactly 7 cm taller than y). Check whether the relation R is reflexive, symmetric or transitive on A.

An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

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

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

Let w denote the words in the english dictionary. Define the relation R by: R = {(x,y) in W xx W | words x and y have at least one letter in common}. Then R is: (1) reflexive, symmetric and not transitive (2) reflexive, symmetric and transitive (3) reflexive, not symmetric and transitive (4) not reflexive, symmetric and transitive