Home
Class 12
MATHS
Prove that the relation R on Z defined b...

Prove that the relation `R` on `Z` defined by `(a ,\ b) in RhArr` `a-b` is divisible by 5 is an equivalence relation on `Z` .

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1b|20 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1c|9 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

Define an equivalence relation.

Show that the relation R defined by R={(a , b):a-b is divisible by 3; a , bZ} is an equivalence relation.

Show that the relation R defined by R={(a , b):a-b is divisible by 3; a , bZ} is an equivalence relation.

Show that the relation R defined by R={(a , b):a-b is divisible by 3; a , bZ} 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 by 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 fixed positive integer. Define a relation R on Z as follows: (a ,\ b) in RhArra-b is divisible by ndot Show that R is an equivalence relation on Zdot

Let n be a fixed positive integer. Define a relation R on Z as follows: (a ,\ b) in RhArra-b is divisible by ndot Show that R is an equivalence relation on Zdot

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.

NAGEEN PRAKASHAN ENGLISH-RELATIONS AND FUNCTIONS -Exercies 1a
  1. Give an example of a relation. Which is (i) Symmetric but neither r...

    Text Solution

    |

  2. If A= {x,y,z}, B=(1,2,3} and R= {(x,2),(y,3),(z,1),(z,2), then find R^...

    Text Solution

    |

  3. Prove that the relation R on Z defined by (a ,\ b) in RhArr a-b is di...

    Text Solution

    |

  4. Prove that the relation R={(x,y): x, y in N and x-y " is divisible by ...

    Text Solution

    |

  5. (i) Prove that the relation ""(x)R(y) iff 3 is a factor of (x-y) , de...

    Text Solution

    |

  6. If I is the set of real numbers, then prove that the relation R={(x,y)...

    Text Solution

    |

  7. If A={a,b,c,d}, then on A . (i) write the identity relation I(A) . ...

    Text Solution

    |

  8. Show that the relation geq on the set R of all real numbers is ref...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. (i) Show that in the set of positive integer, the relation ' greater t...

    Text Solution

    |

  12. Show that the relation is congruent to on the set of all triangles ...

    Text Solution

    |

  13. Show that the relation geq on the set R of all real numbers is ref...

    Text Solution

    |

  14. Let R be relation difined on the set of natural number N as follows, R...

    Text Solution

    |

  15. Let a relation R be defined by relation The R = {(4, 5), (1,4), (4, 6)...

    Text Solution

    |

  16. If A={1,2,3,5}, B={2,4,6,8} and C={4,16,36,39} are three sets and R i...

    Text Solution

    |

  17. Show that the relation R in the set R of real numbers, defined at R={...

    Text Solution

    |

  18. If R1and R2are equivalence relations in a set A, show that R1nnR2is ...

    Text Solution

    |