Home
Class 12
MATHS
Let O be the origin. We define a rela...

Let `O` be the origin. We define a relation between two points `P` and `Q` in a plane if `O P=O Qdot` Show that the relation, so defined is 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

Define an equivalence relation.

Let O be the origin. We define a relation between two points P and Q in a plane if O P=O Q . Show that the relation, so defined is an equivalence relation.

The relation between Q_(3) and P_(75) is

Let A = {p, q, r}. Which of the following is an equivalence relation on A?

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.

What is an equivalence relation? Show that the relation of'similarity' on the set S of all triangle in a plane is an equivalence relation.

Show that the relation ‘is congruent to’ on the set of all triangles in a plane is an equivalence relation

What is the relation in between o-cresol and anisol :

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Show that the relation geq on the set R of all real numbers is r...

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Three relations R1, R2a n dR3 are defined on set A={a , b , c} as foll...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. The following relation is defined on the set of real number: a R ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Let A={1,2,3,ddot,9} and R be the relation in AxA defined by (a ,b)R(c...

    Text Solution

    |

  19. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

    Text Solution

    |

  20. Let n be a positive integer. Prove that the relation R on the set Z o...

    Text Solution

    |