Home
Class 12
MATHS
An integer m is said to be related to an...

An integer `m` is said to be related to another integer `n` if `m` is a multiple of `n` . Check if the relation is symmetric, reflexive and transitive.

Text Solution

Verified by Experts

Here, `R = {(m,n):a,b in Z and m` is a multiple of `n}`
For all `a in R`,
`=> a` will be multiple of `a`.
`:. (a,a) in R`.So, `R` is refexive.

Since in `R` for every `(a,b) in R`
`=> a` is a multiple of `b`.> ...
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|422 Videos
  • SCALAR OR DOT PRODUCT

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is: (A) reflexive and symmetric (B) reflexive and transitive (C) symmetric and transitive (D) equivalence relation

Give an example of a relation which is symmetric but neither reflexive nor transitive.

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

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

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

Every relation which is symmetric and transitive is also reflexive.

m is said to be related to n if m and n are integers and m-n is divisible by 13. Does this define an equivalence relation?

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let Z be the set of all integers and Z0 be the set of all non=zero...

    Text Solution

    |

  2. Let R be the equivalence relation in the set A={0,1,2,3,4,5} given ...

    Text Solution

    |

  3. An integer m is said to be related to another integer n if m is a mult...

    Text Solution

    |

  4. Show that the relation geq on the set R of all real numbers is r...

    Text Solution

    |

  5. m is said to be related to n if m and n are integers and m-n is divisi...

    Text Solution

    |

  6. Let O be the origin. We define a relation between two points P and ...

    Text Solution

    |

  7. Show that the relation R defined by R={(a , b):a-b is divisible ...

    Text Solution

    |

  8. Prove that a relation R on a set A is symmetric iff R=R^-1

    Text Solution

    |

  9. Three relations R1, R2 and R3 are defined on set A={a , b , c} as foll...

    Text Solution

    |

  10. Let a relation R1 on the set R of real numbers be defined as (a , b) ...

    Text Solution

    |

  11. Let S be the set of all points in a plane and R be a relation on S def...

    Text Solution

    |

  12. The following relations are defined on the set of real number: a ...

    Text Solution

    |

  13. Prove that every identity relation on a set is reflexive, but the c...

    Text Solution

    |

  14. Let R be a relation defined on the set of natural numbers N as R={(...

    Text Solution

    |

  15. Let N denote the set of all natural numbers and R be the relation on N...

    Text Solution

    |

  16. Let N be the set of all natural numbers and let R be a relation on N×N...

    Text Solution

    |

  17. Let R be a relation on the set of all line in a plane defined by (l1, ...

    Text Solution

    |

  18. Each of the following defines a relation on N: x -> y , (i) x , y in ...

    Text Solution

    |

  19. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

    Text Solution

    |

  20. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

    Text Solution

    |