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Show that the relation R on the set A of...

Show that the relation `R` on the set `A` of all the books in a library of a college given by `R={(x ,\ y): x` and `y` have the same number of pages}, is an equivalence relation.

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Set A is the set of all books in the library of a college.

`{R}=\{(x, y): x and y` have the same number of pages `\}`

Now, `R` is reflexive since `(x, x) \in R` as `x` and `x` has the same number of pages.

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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Show that the relation R defined on the set A of all triangles in a pl...

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  2. Let n be a positive integer. Prove that the relation R on the set Z o...

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  3. Show that the relation R on the set A of all the books in a library of...

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  4. Show that the relation R on the set A={1,\ 2,\ 3,\ 4,\ 5} , given by R...

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  5. Show that the relation R on the set A={x in Z :0lt=xlt=12} , given by...

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  6. Show that the relation R on the set A of points in a plane, given by R...

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  7. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ <=>(c ...

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  8. Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ...

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  9. Let N be the set of all natural numbers and let R be a relation on Nxx...

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  10. Let N denote the set of all natural numbers and R be the relation on ...

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  11. Prove that the relation congruence modulo m on the set Z of all int...

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  12. Show that the number of equivalence relations on the set {1, 2, 3} ...

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  13. Given a non-empty set X , consider P\ (X) which is the set of all subs...

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  14. Let R be the equivalence relation in the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5}...

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  15. On the set N of all natural numbers, a relation R is defined as follow...

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  16. Show that the relation R defined by R={(a , b):a-b is divisible ...

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  17. Show that the relation R on the set Z of integers, given by R={(a ,\ b...

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  18. Prove that the relation R on Z defined by (a ,\ b) in RhArr a-b is di...

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  19. Let n be a fixed positive integer. Define a relation R on Z as follows...

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  20. Let Z be the set of integers. Show that the relation R={(a ,\ b): a ,\...

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