Home
Class 12
MATHS
In order that a relation R defined on a ...

In order that a relation R defined on a non-empty set A is an equivalence relation. It is sufficient, if R

A

is reflective

B

is symmetric

C

is transitive

D

possesses all the above three properties

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos
  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|6 Videos
  • AREAS OF BOUNDED REGIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos
  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|53 Videos

Similar Questions

Explore conceptually related problems

If R is an equivalence relation on a set A, then R^-1 is

Which one of the following relations on R is an equivalence relation?

(i) Prove that the relation ""_(x)R_(y) iff 3 is a factor of (x-y) , defined on the set of integers is an equivalence relation. (ii) If x is the set of real numbers, then prove that the relation R={(a,b): a in x, b in x and a=b} is an equivalence relation.

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 .

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.

Which of one of the following relations on R is equivalence relation

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

Statement-1: If R is an equivalence relation on a set A, then R^(-1) is also an equivalence relation. Statement-2: R = R^(-1) iff R is a symmetric relation.

OBJECTIVE RD SHARMA ENGLISH-CARTESIAN PRODUCT OF SETS AND RELATIONS -Exercise
  1. Let P={(x,y)|x^(2)+y^(2)=1, x,y in R}. Then, P is

    Text Solution

    |

  2. Let R = {(a, a)} be a relation on a set A.Then R is

    Text Solution

    |

  3. Which one of the following relations on R is an equivalence relation?

    Text Solution

    |

  4. Let X be a family of sets and R be a relation on X defined by A is dis...

    Text Solution

    |

  5. If R is an equivalence relation on a set A, then R^-1 is

    Text Solution

    |

  6. Let R and S be two non-void relations on a set A. Which of the followi...

    Text Solution

    |

  7. If R be a relation lt from A = {1, 2, 3, 4} to B = {1, 3, 5}, i.e. (a,...

    Text Solution

    |

  8. If R is a relation from a set A to a set B and S is a relation from B ...

    Text Solution

    |

  9. If R sub A xx B and S sub B xx C be two relations, then (SoR)^-1 =

    Text Solution

    |

  10. In the set A = {1, 2, 3, 4, 5}, a relation R is defined by R = {(x, y)...

    Text Solution

    |

  11. Let A = {p, q, r}. Which of the following is not an equivalence relati...

    Text Solution

    |

  12. In order that a relation R defined on a non-empty set A is an equivale...

    Text Solution

    |

  13. Let R be a relation on the set N of natural numbers defined by n\ R\ m...

    Text Solution

    |

  14. Let R and S be two non-void relations on a set A. Which of the followi...

    Text Solution

    |

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

    Text Solution

    |

  16. Let L be the set of all straight lines in the Euclidean plane. Two lin...

    Text Solution

    |

  17. For real numbers x and y , define x\ R\ y iff x-y+sqrt(2) is an irrati...

    Text Solution

    |

  18. Let X = {1, 2, 3, 4} and Y = {1, 3, 5, 7,9}. Which of the following is...

    Text Solution

    |

  19. Let n be a fixed positive integer. Define a relation R on Z as follows...

    Text Solution

    |

  20. Let L denote the set of all straight lines in a plane. Let a relation ...

    Text Solution

    |