Home
Class 12
MATHS
A relation R is defined on the set of na...

A relation R is defined on the set of natural numbers `NN` as follows :
`(x,y)in R rArr y` is divisible by x, for all x,`y in NN`.
Show that, R is reflexive and transitive but not symmetric on `NN`.

Promotional Banner

Similar Questions

Explore conceptually related problems

A relation R is defined on the set NN of natural number follows : (x,y) in R implies x divides y for all x,y in NN show that R is reflexive and transitive but not symmetric on NN .

A relation R is defined on the set of natural numbers NN as follows : R {(x,y) : x in NN and x is a multiple of y }. Prove that R is reflexive, antisymmetric and transitive but not symmetric on NN .

A relation R is defined on the set of natural numbers NN follows : (x,y) in R implies x+y =12 for all x,y in NN Prove that R is symmetric but neither reflexive nor transitive on NN .

A relation R is defined on the set N N of natural number follows : (x,y) in "R" implies x+2y=10, for all x,y in N N Show that R is antisymmetric on N N

A relation R is defined on the set of all natural numbers NN by : (x,y) in Rimplies (x-y) is divisible by 6 for all x,y,in NN prove that R is an equivalence relation on NN .

A relation R on the set of natural number N N is defined as follows : (x,y) in R to (x-y) is divisible by 5 for all x,y in N N Prove that R is an equivalence relation on N N .

A relation R is defined on the set of all natural numbers IN by: (x,y)inRimplies(x-y) is divisible by 5 for all x,y inIN . Prove that R is an equivalence relation on IN.

A relation R is defined on the set N N of natural as follows : (x,y) in "R" implies x-y+ sqrt(3) is an iR Rational number for all x,y in N N . Show that R is reflexive on N N .

A relation R is defined on the set of natural numbers N N as follows R = {(x,y) : x,y in N N and x+3y=12} Show that R is transitive and antisymmetric but neither reflexive nor symmetric on N N .

The relation R is defined on the set of natural numbers N as x is a factor of y where x, y in N. Then R is -