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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 obove three properties

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The correct Answer is:
D
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TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. Let A = {x,y,z} and B = {a,b,c,d} . Which one of the following is not ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. For any two numbers theta and phi , we define theta R phi ...

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