Home
Class 12
MATHS
Prove that a relation R on a set A is sy...

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

A

Reflexive

B

Symmetric

C

Transitive

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 2: Mappings, Mapping of Functions, Kinds of Mapping of Functions)|19 Videos

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 3: Composite Function and Relation, Inverse of a Function, Binary Operations)|27 Videos

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos

  • RELATIONS AND FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE - 2|30 Videos

  • SEQUENCES AND SERIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

Let R={(a,a)} be a relation on a set A.Then R is

Prove that the relation R in the set A={1,2,3,4,5,6,7} given by R={(a,b):|a-b|iseven} is an equivalence relation.

Knowledge Check

  • 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]"

    A
    Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for statement-1.
    B
    Statement-1 is True, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
    C
    Statement-1 is True, Statement-2 is False
    D
    Statement-1 is False, Statement-2 is True.

  • 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.

    A
    Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for statement-1.
    B
    Statement-1 is True, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
    C
    Statement-1 is True, Statement-2 is False
    D
    Statement-1 is False, Statement-2 is True.

    • Similar Questions

    Explore conceptually related problems

    Show that the relation R on the set A={1,2,3} given by R={(1,2),(2,1)} is symmetric but neither reflexive nor transitive.

    If R is a symmetric relation on a set A, then write a relation between R and R^(-1) .

    Prove that the relation R defined on the set N of natural numbers by xRy iff 2x^(2) - 3xy + y^(2) = 0 is not symmetric but it is reflexive.

    Show that the relation R in the set R of real numbers,defined as R={(a,b):a<=b^(2)} is neither reflexive nor symmetric nor transitive.

    Show that the relation R on the set A{x in Z;0<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

    Show that the relation R in the set {1,2,3} given by R={(1,2),(2,1)} is symmetric but neither reflexive nor transitive.

    Home
    Profile