Home
Class 12
MATHS
If R is a relation on the set A={1,2,3} ...

If R is a relation on the set `A={1,2,3}` given by `R={(1,1),(2,2),(3,3)}`, then R is

A

symmetric only

B

reflexive only

C

an equivalence relation

D

transitive only

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, R is the identify relation on set {1, 2, 3} and the identity relation is always an equivalence relation. Hence, R is an equivalence relation.
Promotional Banner

Topper's Solved these Questions

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|6 Videos

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|38 Videos

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 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 a relation on the set A={1,2,3} given by R={(1,1),(1,2),(2,1)} , then R is

If R is a reation on the set A={1,2,3} given by R={(1,1),(2,2)(1,3)} then R is

If R is a relation on the set A={1,2,3} given by R={(1,1),(2,2),(3,3),(1,2)(2,3),(1,3)} , then R is

If R is a relation on the set A={1,2,3} defined by R={(1,2)} , then R is

Show that the relation R on the set A={1,\ 2,\ 3} given by R={(1,\ 1),\ (2,\ 2),\ (3,\ 3),\ (1,\ 2),\ (2,3\ )} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

Let R be the relation on the set A={1,\ 2,\ 3,\ 4} given by R={(1,\ 2),\ (2,\ 2),\ (1,\ 1),\ (4,\ 4),\ (1,\ 3),\ (3,\ 3),\ (3,\ 2)} . Then, R is reflexive and symmetric but not transitive (b) R is reflexive and transitive but not symmetric (c) R is symmetric and transitive but not reflexive (d) R is an equivalence relation

Let R be the relation on the set A={1,\ 2,\ 3,\ 4} given by R={(1,\ 2),\ (2,\ 2),\ (1,\ 1),\ (4,\ 4),\ (1,\ 3),\ (3,\ 3),\ (3,\ 2)} . Then, R is (a) reflexive and symmetric but not transitive (b) R is reflexive and transitive but not symmetric (c) R is symmetric and transitive but not reflexive (d) R is an equivalence relation

lf a relation R on the set {1, 2, 3} be defined by R ={(1,2)} , then R is:

Show that the relation R on the set A={1,\ 2,\ 3} given by R={(1,\ 2),\ (2,\ 1)} is symmetric but neither reflexive nor transitive.

OBJECTIVE RD SHARMA ENGLISH-CARTESIAN PRODUCT OF SETS AND RELATIONS -Section I - Solved Mcqs
  1. If A={x:x^(2)-5x+6=0},B={2,4},C={4,5} then find Axx(BnnC)

    Text Solution

    |

  2. If A={a,b},B={c,d},C={d,e}, then {(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)}...

    Text Solution

    |

  3. If R is a relation on the set A={1,2,3} given by R={(1,1),(2,2),(3,3)}...

    Text Solution

    |

  4. The relation R defined on the set A={1,\ 2,\ 3,\ 4,\ 5} by R={(a ,\ b)...

    Text Solution

    |

  5. Let Y={1,2,3,4,5}, A={1,2}, B={3,4,5}. If (A xx B) denotes Cartesian p...

    Text Solution

    |

  6. Let A={2,\ 3,\ 4,\ 5,\ .......\ 17 ,\ 18} . Let ' ' be the equivalenc...

    Text Solution

    |

  7. Let S be the set of all real numbers. Then , the relation R = {(a, b) ...

    Text Solution

    |

  8. Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9(,(3,12),(3,6)} be relatio...

    Text Solution

    |

  9. Let R be the real line. Consider the following subsets of the plane ...

    Text Solution

    |

  10. Let w denotes the set of words in the English dictionary. Define the r...

    Text Solution

    |

  11. On the set N of natural numbers, delined the relation F by a R b if th...

    Text Solution

    |

  12. The relation R defined on the set A={1,\ 2,\ 3,\ 4,\ 5} by R={(a ,\ b)...

    Text Solution

    |

  13. The relation on the set A={x|x|<3,x,in Z} is defined by R={(x,y);y=|x|...

    Text Solution

    |

  14. The number of equivalence relations defined in the set S = {a, b, c} i...

    Text Solution

    |

  15. Let R be a relation on the set of integers given by aRb<=> a= 2^k.b f...

    Text Solution

    |

  16. Consider the following relations: R={(x,y)|(x,y " are real numbers ...

    Text Solution

    |

  17. Let N be the set of natural numbers and for a in N, aN denotes the set...

    Text Solution

    |

  18. Let A and B be two sets containing four and two elements, respectively...

    Text Solution

    |

  19. If the numbers of different reflexive relations on a set A is equal to...

    Text Solution

    |

  20. Let R = {(x, y) : x, y in N and x^2-4xy+3y^2 = 0}, where N is the set...

    Text Solution

    |