Home
Class 12
MATHS
Let R be a relation on the set A of orde...

Let `R` be a relation on the set `A` of ordered pairs of integers defined by `(x ,\ y)\ R\ (u ,\ v)` iff `x v=y udot` Show that `R` is an equivalence relation.

Text Solution

Verified by Experts

First let `R` be a relation on `A`

Given as set A of ordered pair of integers defined by `(x, y) R(u, v)` if `x v=y u`

Let us check whether the given relation is equivalence or not.

...
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

Let R be a relation on the set A of ordered pairs of positive integers defined by (x,y)R(u,v) if and only if xv=yu Show that R is an equivalence relation.

Let R be a relation on the set of all real numbers defined by xRy hArr|x-y|<=(1)/(2) Then R is

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is

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 hArr x-y is divisible by n, is an equivalence relation on Z .

Let R be the relation on the set R of all real numbers defined by a Rb Iff |a-b|<=1 Then R is

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 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.

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let Z be the set of integers. Show that the relation R={(a ,\ b): a ,\...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If A={2,\ 3,\ 4} , B={1,\ 3,\ 7} and R={(x ,\ y): x in A ,\ y in B\ ...

    Text Solution

    |