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Let R be the set of real numbers. Stat...

Let R be the set of real numbers.
Statement 1:`A={(x,y) in R xx R : y-x` is an integer} is an equivalence relation on R.
Statement 2: `B= {x,y} in Rxx R : x=alpha y` for some rational number `alpha`} is an equivalence relation on R.

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ML KHANNA-CONCEPTS OF SET THEORY -Problem Set (2) (RELATIONS)
  1. Let R be a relation on I (the ste of integers) defined as m R n (m,nin...

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

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

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  4. An integer m is said to be related to another integer n if m is a m...

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  5. If alpha,beta be straight lines in a plane, then check R(1)andR(2) for...

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  6. Let n be a fixed positive integer. Define a relation R on I (the set o...

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  7. Consider the non-empty set consisting of children in a family. State g...

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  8. Consider the non-empty set consisting of children in a family. State g...

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  9. Let S be the set of all points in a plane. Let R be a relation on S s...

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  10. N is the set of natural numbers. The relation R is defined on NxxN as ...

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  11. N is the set of positive intergers and ~ be a relation on NxxN defined...

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  12. The following relation is defined on the set of real numbers. A R b if...

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  13. If R be a relation a R b if 1+abgt0. What about equivalence relation ?

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  14. A relation R on the set of complex numbers is defined by z1 R z2 if ...

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

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  16. On the set of all points in a plane, the relation defined by the phras...

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  17. A function R on the set N of natural numbers is defined as R={[2n,2n+1...

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  18. A relation f on the set N of natural numbers is defined by f={(n,n+3):...

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  19. Consider the following relations: R = {(x, y) | x, y are real numbers ...

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  20. Let R be the set of real numbers. Statement 1:A={(x,y) in R xx R : y...

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