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

Show that the relation `R` on the set `A` of points in a plane, given by `R={(P ,\ Q):` Distance of the point `P` from the origin is same as the distance of the point `Q` from the origin}, is an equivalence relation. Further show that the set of all points related to a point `P!=(0,\ 0)` is the circle passing through `P` with origin as centre.

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Show that the relation R on the set A={1,\ 2,\ 3,\ 4,\ 5} , given by R...

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

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  3. Show that the relation R on the set A of points in a plane, given by 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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  5. Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ...

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

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

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

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

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

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

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

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

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

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

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

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

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  18. m is said to be related to n if m and n are integers and m-n is divisi...

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  19. Let R be a relation on the set A of ordered pairs of integers defined ...

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

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