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Let A={1,2,3,.....,9} and R be the relat...

Let `A={1,2,3,.....,9}` and `R` be the relation in `AxxA` defined by `(a ,b)R(c ,d)` if `a+d=b+c` for `(a ,b),(c , d)` in `AxxAdot` Prove that `R` is an equivalence relation. Also obtain the equivalence class [(2,5)].

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Let `A={1,2,3, ldots, 9)`

`forall(a, b) in A times A`

`a+b =b+a`

`therefore(a, b) R(a, b)`

...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
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  2. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

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  3. Let A={1,2,3,.....,9} and R be the relation in AxxA defined by (a ,b)R...

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  4. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

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

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  12. If R={(x,y):x+2y=8} is a relation on N, write the range of R.

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  13. Let Z be the set of all integers and R be the relation on Z defi...

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  14. The union of two equivalence relations on a set is not necessarily an ...

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  15. Let A be the set of all students of a boys school. Show that the re...

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

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  17. The relation R on the set N of all natural numbers defined by (x ,\ y)...

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  18. Three relations R1, R2a n dR3 are defined on set A={a , b , c} as foll...

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  19. Show that the relation R on the set A={1,\ 2,\ 3} given by R={(1,\ 1),...

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  20. Show that the relation R on the set A={1,\ 2,\ 3} given by R={(1,\ 2),...

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