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Let R be the real line, Consider the fol...

Let R be the real line, Consider the following subsets of the plane `R xx R` :
`S = {(x, y) : y = x + 1 " and " 0 lt x lt 2}`
`T = {(x, y) : x - y` is an integer}.
Which one of the following is true ?

A

T is an equivalence relation on R but S is not

B

Neither S nor T is an equivalence relation on R

C

Both S and T are equivalence relations on R

D

S is an equivalence relation on R but T is not.

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The correct Answer is:
A
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MODERN PUBLICATION-RELATIONS-MCQ LEVEL-II
  1. Let R be a relation in the set of natural numbers defined by R= {(1+x,...

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  2. R is a relation over the set of real numbers and it is given by mn ge ...

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  3. R is a relation over the set of integers and it is given by (x,y) in R...

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  4. Let L be the set of all straight lines in the Euclidean plane. Two lin...

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  5. Let R be the relation over the set of straight lines in a plane such t...

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  6. Let R be the relation over the set of integers such that l R m iff l i...

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

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  8. Let R ={(x,y) : x,y in A, x+y=5}, where A= {1,2,3,4,5}. Then :

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  9. For x,y in R, define a relation R by x R y if and only if x-y+sqrt(2) ...

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  10. Given the relation R= {(1,2),(2,3)} is the set A= {1,2,3}. Then the mi...

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  11. Let A= {a,b,c}. Which of the following is not an equivalence relation ...

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  12. Let R1 and R2 be two equivalence relations in the set A. Then:

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  13. If A is the set of even natural numbers less than 8 and B is the set o...

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  14. Let R= {(1,3), (4, 2), (2, 4), (2, 3) , (3, 1)} be a relation on the s...

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  15. Let R= { (3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3,9), (3, 12), (...

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  16. Let x,y in I and suppose that a relation R on I is defined by x R y if...

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  17. The relation R defined on the set A = { 1, 2, 3, 4} by : R= {( x,y)...

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  18. Let S be the set of all real numbers. Then the relation R = {(a, b) : ...

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  19. Let W denote the words in the English dictionary. Define the relation ...

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  20. Let R be the real line, Consider the following subsets of the plane R...

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