Home
Class 12
MATHS
m is said to be related to n if m and n ...

`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?

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|449 Videos

  • SCALAR OR DOT PRODUCT

    RD SHARMA ENGLISH|Exercise All Questions|233 Videos

Similar Questions

Explore conceptually related problems

Let Z be the set of all integers and R be the relation on Z defined by R= { (a,b): a, b in Z and (a-b) is divisible by 5} . Prove that R is an equivalence relation

Let Z be the set of all integers and R be the relation on Z defined as R={(a, b); a,\ b\ in Z, and (a-b) is divisible by 5} . Prove that R is an equivalence relation.

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Let m be a given fixed positive integer. Let R={(a.b) : a,b in Z and (a-b) is divisible by m} . Show that R is an equivalence relation on Z .

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.

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.

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let n be a fixed positive integer. Define a relation R on Z as follows...

    Text Solution

    |

  2. Let Z be the set of integers. Show that the relation R={(a ,\ b): a ,\...

    Text Solution

    |

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

    Text Solution

    |

  4. Let R be a relation on the set A of ordered pairs of integers defined ...

    Text Solution

    |

  5. Show that the relation R on the set A={x in Z ;0lt=xlt=12} , given by...

    Text Solution

    |

  6. Let L be the set of all lines in X Y -plane and R be the relation in L...

    Text Solution

    |

  7. Show that the relation R , defined on the set A of all polygons as R={...

    Text Solution

    |

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

    Text Solution

    |

  9. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

    Text Solution

    |

  10. Let S be a relation on the set R of all real numbers defined by S={(a ...

    Text Solution

    |

  11. Let Z be the set of all integers and Z0 be the set of all non-zero int...

    Text Solution

    |

  12. If R and S are relations on a set A , then prove the following: R and ...

    Text Solution

    |

  13. If R and S are transitive relations on a set A , then prove that RuuS ...

    Text Solution

    |

  14. Write the domain of the relation R defined on the set Z of integers as...

    Text Solution

    |

  15. If R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z} is a relation on Z , write ...

    Text Solution

    |

  16. Write the identity relation on set A={a ,\ b ,\ c} .

    Text Solution

    |

  17. Write the smallest reflexive relation on set A={1,\ 2,\ 3,\ 4} .

    Text Solution

    |

  18. If R={(x ,\ y): x+2y=8} is a relation on N , then write the range of R...

    Text Solution

    |

  19. If R is a symmetric relation on a set A , then write a relation betwee...

    Text Solution

    |

  20. Let R={(x ,\ y):|x^2-y^2|<1} be a relation on set A={1,\ 2,\ 3,\ 4,\ 5...

    Text Solution

    |