Home
Class 12
MATHS
If R is an equivalence relation on a set...

If R is an equivalence relation on a set A, then `R^-1` is A. reflexive only B. symmetric but not transitive C. equivalence D. None of these

Text Solution

Verified by Experts

Consider` A = {a, b, c}`

`R: {(a, a}, (b, b), (c, c), (a, b), (b, a), (a, c), (c, a), (b, c), (c, a)}`

`R^-1 = {(a, a}, (b, b), (c, c), (b, a), (a, b), (c, a), (a, c), (c, b), (a, c)}`

`R^-1` is reflexive, symmetric and transitive.

...
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

If R and S are two equivalence relations on a set A then R nn S is also an equivalence relation on R.

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a\ R\ b if a is congruent to b for all a ,\ b in T . Then, R is (a) reflexive but not symmetric (b) transitive but not symmetric (c) equivalence (d) none of these

Let R and S be two equivalence relations on a set A Then : " " A. R uu S is an equvalence relation on A " " B. R nn S is an equirvalence relation on A " " C. R - S is an equivalence relation on A " " D. None of these

If R and R' are symmetric relations (not disjoint) on a set A ,then the relation R uu R' is (i) Reflexive (ii) Symmetric (ii) Transitive (iv) none of these

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.

Consider that the set A = {a, b, c} . Give an example of a relation R on A. Which is : (i)reflexive and symmetric but not transitive (ii) symmetric and transitive but not reflexive (iii) reflexive and transitive but not symmetric.

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

Let M be the set of men and R is a relation is son of defined on M.Then,R is ( a) an equivalence relation (b) a symmetric relation (c) a transitive relation (d) None of these

In a set of real numbers a relation R is defined as xRy such that |x|+|y|<=1 then relation R is reflexive and symmetric but not transitive symmetric but not transitive and reflexive transitive but not symmetric and reflexive (4) none of reflexive,symmetric and transitive

Statement-1: On the set Z of all odd integers relation R defined by (a, b) in R iff a-b is even for all a, b in Z is an equivalence relation. Statement-2: If a relation R on a set A is symmetric and transitive, then it is reflexive and hence an equivalence relation, because (a, b) in Rimplies(b, a)in R" [By symmetry]" (a, b)in R and (b, a) in Rimplies (a,a)in R " [By transitivity]"

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Prove that every identity relation on a set is reflexive, but the c...

    Text Solution

    |

  2. Let Z be the set of integers. Show that the relation R={(a , b): a ...

    Text Solution

    |

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

    Text Solution

    |

  4. On the set N of all natural numbers, a relation R is defined as follow...

    Text Solution

    |

  5. If R1 and R2 are equivalence relations in a set A, show that R1nnR2...

    Text Solution

    |

  6. Let Z be the set of all integers and Z0 be the set of all non=zero...

    Text Solution

    |

  7. Let R be the equivalence relation in the set A={0,1,2,3,4,5} given ...

    Text Solution

    |

  8. An integer m is said to be related to another integer n if m is a mult...

    Text Solution

    |

  9. Show that the relation geq on the set R of all real numbers is r...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Three relations R1, R2 and R3 are defined on set A={a , b , c} as foll...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. The following relations are defined on the set of real number: a ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |