Home
Class 12
MATHS
Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (2,\ ...

Let `A={1,\ 2,\ 3}` and `R={(1,\ 2),\ (2,\ 3),\ (1,\ 3)}` be a relation on `A` . Then, `R` is (a)neither reflexive nor transitive (b)neither symmetric nor transitive (c) transitive (d) none of these

Text Solution

Verified by Experts

The correct Answer is:
c) transitive
The given relation is not reflexive as `(1,1),(2,2),(3,3)in R.`
Again the relation is not symmetric as `(1,2) in R` but `(2,1) in R.`
But the relation is transitive as `(1,2) in {R},(2,3) in {R}`
` Rightarrow(1,2) in {R} forall 1,2, in {A}`.
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

2. If A={a,b,c} and R={(a, a),(a, b),(a, c), (b, c)}be a relation on A, then R is(a) reflexive (b) transitive (C) symmetric (d) none of these Tatooidh... TU

Let A={1,\ 2,\ 3} and consider the relation R={(1,\ 1),\ (2,\ 2),\ (3,\ 3),\ (1,\ 2),\ (2,\ 3),\ (1,\ 3)} . Then, R is (a) reflexive but not symmetric (b) reflexive but not transitive (c) symmetric and transitive (d) neither symmetric nor transitive

If A={1, 2, 3} , then a relation R={(2,3)} on A is (a) symmetric and transitive only (b) symmetric only (c) transitive only (d) none of these

Let A={1,2,3,4}R={(2,2),(3,3),(4,4),(1,2)} be a relation on A.Then R is 1) reflexive 2) symmetric 3 ) transitive 4 ) Both 1 & 2

Let A = {1,2,3} and R be a relation on A defind as R = {(1,2), (2,3),(1,3)} , then R is (a) reflexive (b) symmetric (c) transtive (d) none of these

6.In the set A={1,2,3,4,5), a relation R is defined by R={(x,y):x, ye Aand rlty }. Then R is (a) reflexive (b) symmetric (c) transitive (d) none of these

Give an example of a relation which is symmetric but neither reflexive nor transitive.

Show that the relation < in the set of positive integers is transitive,but it is neither symmetric nor reflexive.

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 A={1, 2, 3) be a given set. Define a relation on A swhich is (i) reflexive and transitive but not symmetric on A (ii) reflexive and symmeetric but not transitive on A (iii) transitive and symmetric but not reflexive on A (iv) reflexive but neither symmetric nor transitive on A (v) symmetric but neither reflexive nor transitive on A (vi) transitive but neither reflexive nor symmetric on A (vii) neither reflexive nor symmetric and transitive on A (vii) an equivalence relation on A (ix) neither symmetric nor anti symmmetric on A (x) symmetric but not anti symmetric on A

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. R is a relation from {11, 12, 13} to {8, 10, 12} defined by y=x-3 ....

    Text Solution

    |

  2. Let R={(a ,\ a),\ (b ,\ b),\ (c ,\ c),\ (a ,\ b)} be a relation on set...

    Text Solution

    |

  3. Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (2,\ 3),\ (1,\ 3)} be a relation on...

    Text Solution

    |

  4. If R is the largest equivalence relation on a set A and S is any relat...

    Text Solution

    |

  5. If R is a relation on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} gi...

    Text Solution

    |

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

    Text Solution

    |

  7. If A={a ,\ b ,\ c ,\ d}, then a relation R={(a ,\ b),\ (b ,\ a),\ (a ,...

    Text Solution

    |

  8. If A={1, 2, 3} , then a relation R={(2,3)} on A is (a) symmetric and t...

    Text Solution

    |

  9. Let R be the relation on the set A={1,\ 2,\ 3,\ 4} given by R={(1,\ 2)...

    Text Solution

    |

  10. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  11. The relation R={(1,\ 1),\ (2,\ 2),\ (3,\ 3)} on the set {1, 2, 3} is (...

    Text Solution

    |

  12. S is a relation over the set R of all real numbers and it is given by ...

    Text Solution

    |

  13. In the set Z of all integers, which of the following relation R is not...

    Text Solution

    |

  14. Let A={1,\ 2,\ 3} and consider the relation R={(1,\ 1),\ (2,\ 2),\ (3,...

    Text Solution

    |

  15. The relation S defined on the set R of all real number by the rule a\ ...

    Text Solution

    |

  16. The maximum number of equivalence relations on the set A = {1, 2, 3} a...

    Text Solution

    |

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

    Text Solution

    |

  18. Let L denote the set of all straight lines in a plane. Let a relatio...

    Text Solution

    |

  19. Let T be the set of all triangles in the Euclidean plane, and let a...

    Text Solution

    |

  20. Let R be a relation defined by R={(a, b): a >= b, a, b in R}. The rela...

    Text Solution

    |