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Suppose a box contains a set of n balls `(n gt 4)`(denoted by B )of four different colours (many have different sizes), viz,red, blue, green and yellow. Show that a relation R defined on B as `R={(b_1,b_2) : "balls" b_1 "and" b_2` have the same colour} is an equivalence relation on B. How many equivalence classes can you find with respect ot R ?

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ARIHANT PUBLICATION-RELATIONS AND FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS ( Exercise 1 (a))
  1. Given an example of a relation which is reflexive, symmetric but not...

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  2. Given an example of a relation which is reflexive, transitive but n...

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  3. Given an example of a relation which is symmetric, transitive but no...

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  4. Given an example of a relation which is reflexive but neither symmet...

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  5. Given an example of a relation which is transitive but neither refle...

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  6. Given an example of a relation which is an empty relation.

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  7. Given an example of a relation which is a universal relation.

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  8. Let R be a relation on X, If R is symmetric then xRy impliesyRx. If it...

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  9. Suppose a box contains a set of n balls (n gt 4)(denoted by B )of four...

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  10. Find the number of equivalence, relations on X ={1,2,3),

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  11. Let R be the relation on the set R of real numbers such that aRb iff a...

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  12. Find the least positive integer r such that 185 in [r]7

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  13. Find the least positive integer r such that -375 in [r]11

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  14. Find the least positive integer r such that -12 in [r]13

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  15. Find least non negative integer r such that 7xx13xx23xx413 -= r "(mod ...

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  16. Find least non negative integer r such that 6xx18xx27xx(-225) -= r "(m...

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  17. Find least non negative integer r such that 1237"(mod 4)"+985"(mod 4)"...

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  18. Find least non negative integer r such that 1936xx8789 -= r"(mod4)"

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  19. Find least positive integer x, satisfying 276x+128=4 (mod 7).

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  20. Find three positive integers xi,i=1,1,3 "satisfying" 3x -= 2 "(mod 7)"

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