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 The Straight Lines Exercise 8 : (Questions Asked in Previous 13 years Exams)|1 Videos

Similar Questions

Explore conceptually related problems

If relation R defined on set A is an equivalence relation, then R is

Show that the relation R defined by (a, b) R(c,d)implies a+d=b+c in the set N is an equivalence relation.

Prove that on the set of integers. Z, the relation R defined as aRb hArr a = +-b is an equivalence relation .

If R is a relation in N xx N , show that the relation R defined by (a, b) R (c, d) if and only if ad = bc is an equivalence relation.

The smallest equivalence relation R on set A ={1,2,8} is=

Let R_1 and R_2 be two relations defined on a non-empty set A. Which of the following statements is false? Give reason in support of your answer. If R_1 and R_2 are reflexive, then so is R_! Nn R_2 .

In the following cases, for the given relation R on the set S, determine which are equivalence relations: S is the set of all people in the world today, a R b iff a and b have same father.

In the following cases, for the given relation R on the set S, determine which are equivalence relations: S is the set of all people in the world today, a R b iff a lives within 100 kilometres f b.

Prove that the following relation R in Z of integers is an equivalence relation R = {(x, y): x-y is an integer}

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. Let A={p , q , r , s}\ a n d\ B={1,2,3}dot Which of the following rela...

    Text Solution

    |

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

    Text Solution

    |

  6. Find all congruent solutions of 8x -= 6 (mod 14).

    Text Solution

    |

  7. Let A be a set containing 10 distinct elements. Then the total number ...

    Text Solution

    |

  8. write the value of cos^(-1)(1/2)-sin^(-1)(-1/2)

    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 the number of subjectio...

    Text Solution

    |

  13. If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

    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 function f:AtoB is a bijective , then f^(-1)of is a. fof^(-1) b. f...

    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

    |