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 :
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`.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination ( Multiple CoR Recy Answers Type )|5 Videos
  • RELATIONS

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Integer Answer Type)|5 Videos
  • RELATIONS

    CHHAYA PUBLICATION|Exercise Very short Answer Type Questions|19 Videos
  • RELATION AND FUNCTIONS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|3 Videos
  • REVISION OF PREVIOUS TWO DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams E (Assertion - Reason Type )|2 Videos

Similar Questions

Explore conceptually related problems

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 .

A relation R is defined on the set of natural numbers N as follows: R={(x,y)}|x,y in N and 2x+y=41} show that R is neither reflexive nor symmetric nor transitive.

A relation R is defined on the set of natural numbers N as follows: R={(x,y)|x,yinN " and " 2x+y=41} . Show that R is neither reflexive nor symmetric nor transitive.

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 .

A relation R_(1) is defined on the set of real number R R as follows : R_(1) ={(x,y) : 1+xy gt 0 , x inR R y in R R } Show that R_(1) is reflexive and symmetric but not transitive on R R .

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 -

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 defined on the set of natural no as follows R={(x,y),x+5y=20,x, y in N }.Find in domain and range of R.

A relation R is defined on the set of integers Z as follows: R{(x,y):x,y in Z and x-y" is odd"} Then the relation R on Z is -

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 .

CHHAYA PUBLICATION-RELATIONS-Short Answer Type Questions
  1. A relation R is defined on the set of integers Z Z as follows R= {(x...

    Text Solution

    |

  2. A relation R is defined on the set of all integers Z Z follows : (x,...

    Text Solution

    |

  3. Show that the relation R defined in the set A of all polygons as R = {...

    Text Solution

    |

  4. Let O be the origin. We define a relation S between two points P and Q...

    Text Solution

    |

  5. A relation S is defined on the set of real numbers R R a follows: S=...

    Text Solution

    |

  6. On a given set AA define the smalest and the large equivalence relatio...

    Text Solution

    |

  7. A relation S is defined on the set of real numbers R R a follows : S...

    Text Solution

    |

  8. Let A={ a,b,c} be a given set. Define a relation on A which is : (i...

    Text Solution

    |

  9. Let A={ a,b,c} be a given set. Define a relation on A which is : re...

    Text Solution

    |

  10. Let A={ a,b,c} be a given set. Define a relation on A which is : tr...

    Text Solution

    |

  11. Let A={ a,b,c} be a given set. Define a relation on A which is : re...

    Text Solution

    |

  12. Let A={ a,b,c} be a given set. Define a relation on A which is : sy...

    Text Solution

    |

  13. Let A={ a,b,c} be a given set. Define a relation on A which is : tr...

    Text Solution

    |

  14. Let A={ a,b,c} be a given set. Define a relation on A which is : ne...

    Text Solution

    |

  15. Let A={ a,b,c} be a given set. Define a relation on A which is : a...

    Text Solution

    |

  16. A relation R is defined on the set of natural numbers NN as follows : ...

    Text Solution

    |

  17. Let R and S be two relations on a set A. If (i) R and S are both sym...

    Text Solution

    |

  18. Let R and S be two relations on a set A. If (ii) R is reflexive and ...

    Text Solution

    |

  19. Let R and S be two relations on a set A. If (iii). R and S are both ...

    Text Solution

    |

  20. A relation R is defined on the set N N of natural as follows : (x,y)...

    Text Solution

    |