Home
Class 11
MATHS
R sube A xx A (where A ne 0 ) is an equi...

`R sube A xx A` (where `A ne 0` ) is an equivalence relation if R is

A

Reflexive, symmetric but not transitive

B

Reflexive, niether symmetric nor transitive

C

Reflexive, symmetric and transitive

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|83 Videos

  • PROBABILITY

    TARGET PUBLICATION|Exercise EVALUATION TEST|8 Videos

  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

Similar Questions

Explore conceptually related problems

Prove that relation define on positive integers such as R={(x,y):x-y is divisible by 3 where x,y in N} is an 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 , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq 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

R={(1,2),(2,3),(3,4)} be a relation on the set of natural numbers. Then the least number of elements that must be included in R to get a new relation S where S is an equivalence relation is

Let R be the real line. Consider the following subsets of the plane RxxR . S""=""{(x ,""y)"":""y""=""x""+""1""a n d""0""<""x""<""2},""T""=""{(x ,""y)"":""x-y"" is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not

A relation R is defined on the set of integers as follows : ""_(a)R_(b) hArr(a - b) , is divisible by 6 where a, b, in I. prove that R is an equivalence relation.

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

Let A={1,2,3,~ 9}~ and~ R be the relation on A xx A defined by (a,b)R(c,d) if a+d=b+c for all (a,b),(c,d)in A xx A Prove that R is an equivalence relation and also obtain the equivalence class [(2,5)]

Prove that a relation R defined on N xx N where (a,b)R(c,d)hArr ad=bc is an equivalence relation.

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

TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. Let A and B be two sets containing four and two elements respective...

    Text Solution

    |

  2. Let A = {x,y,z} and B = {a,b,c,d} . Which one of the following is not ...

    Text Solution

    |

  3. R sube A xx A (where A ne 0 ) is an equivalence relation if R is

    Text Solution

    |

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

    Text Solution

    |

  5. The number of reflexive relations of a set with four elements is equal...

    Text Solution

    |

  6. If a relation R on the set N of natural numbers is defined as (x,y)hAr...

    Text Solution

    |

  7. let A = {2,4,6,8}. A relation R on A is defined by R= {(2,6),(6,2),(4,...

    Text Solution

    |

  8. The relation R defined in N as aRbimpliesb is divisible by a is

    Text Solution

    |

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

    Text Solution

    |

  10. The relation S = {(3,3),(4,4)} on the set A ={2,3,4} is "".

    Text Solution

    |

  11. let S ={1,2,3,…,24}. Define a relation '~' on S as x ~y is the product...

    Text Solution

    |

  12. Let R={ (1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2...

    Text Solution

    |

  13. Let R(1) be a relation defined by R(1)={(a,b)|agtb,a,b in R}. Then ...

    Text Solution

    |

  14. Let R be the relation on the set R of all real numbers defined by a R ...

    Text Solution

    |

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

    Text Solution

    |

  16. On the set R of real numbers, the relation p is defined by xpy, ( x ,y...

    Text Solution

    |

  17. Let r be relation from R (set of real numbers) to R defined by r={(a,b...

    Text Solution

    |

  18. On R, a relation p is defined by xpy if and only if x-y is zero or irr...

    Text Solution

    |

  19. On the set N of all natural numbers define the rational R by aRb iff t...

    Text Solution

    |

  20. Let W denote the words in the english dicitionary define the relatio...

    Text Solution

    |