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 reflexive

B

is symmetric

C

is transitive

D

possesses all the above three properties

Text Solution

Verified by Experts

The correct Answer is:
D

By definition for equivalent relation. R should be reflexive, symmetric, transitive.
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|3 Videos
  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|6 Videos
  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 3|10 Videos
  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos
  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

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

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

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

The relation R on R defined as R={(a ,b) : a <=b } is an equivalence relation. State true or false.

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 only (c) a transitive relation only (d) None of the above

Prove that the relation R on Z defined by (a,b)in R hArr a-b is divisible by 5 is an equivalence relation on Z .

Let Z be the set of integers.Show that the relation R={(a,b):a,b in Z and a+b is even } is an equivalence relation on Z .

Let Z be the set of integers.Show that the relation R={(a,b):a,b in Z and a+b is even } is an equivalence relation on Z .

Show that the relation R defined by R={(a,b):a-b is divisible by 3;a,b in Z} is an equivalence relation.

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

ARIHANT MATHS-SETS, RELATIONS AND FUNCTIONS -Exercise (Single Option Correct Type Questions)
  1. The composite mapping fog of the maps f:R to R , f(x)=sin x and g:R to...

    Text Solution

    |

  2. Which of the following is the empty set

    Text Solution

    |

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

    Text Solution

    |

  4. If A = {p,q,r, s} and B = {1, 2, 3}, find which of the following is n...

    Text Solution

    |

  5. For n,mepsilonN,n|m means that n is a factor of m then relation | is

    Text Solution

    |

  6. The solution of 8x = 6 (mod 14) is

    Text Solution

    |

  7. Let A be a set containing 10 distinct elements,then the total number o...

    Text Solution

    |

  8. Let A and B be two non empty subsets of set X such that A is not a sub...

    Text Solution

    |

  9. f and h are function from A rarr B, where A = {a, b, c, d} and B = {s,...

    Text Solution

    |

  10. Let I be the set of integer and f : I rarr I be defined as f(x) = x^(2...

    Text Solution

    |

  11. Which of the four statements given below is different from other?

    Text Solution

    |

  12. Let A={1,2,..., n} and B={a , b }. Then number of subjections from A i...

    Text Solution

    |

  13. Let f:R to R be defined by f(x)=3x-4. Then, f^(-1)(x) is

    Text Solution

    |

  14. f:R to R is a function defined by f(x)=10x -7, if g=f^(-1) then g(x)=

    Text Solution

    |

  15. Let R be a relation defined by R = {(a, b) : a ge b}, where a and b a...

    Text Solution

    |

  16. If the sets A and B are defined are defined as A={(x,y):y=e^x, x in R}...

    Text Solution

    |

  17. If f : A rarr B is a bijective function, then f^(-1) of is equal to

    Text Solution

    |

  18. If f(y) = (y)/(sqrt(1-y^(2))), g(y) = (y)/(sqrt(1+y^(2))), then (fog) ...

    Text Solution

    |

  19. f:R->R is defined as f(x)=2x+|x| then f(3x)-f(-x)-4x=

    Text Solution

    |

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

    Text Solution

    |