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Suppose a box contains a set of n balls ...

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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MBD PUBLICATION-RELATION AND FUNCTION-QUESTION BANK
  1. Given an example of a relation which is a universal relation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Let X ={x,y} and Y ={u,v}. Write down all the functions that can be de...

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  16. Let X and Y be sets containing m and n elements respectively.What is t...

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  17. Let X and Y be sets containing m and n elements respectively.How many ...

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  18. Examine f :R rarr R, f(x) =x^2functions if it is (i) injective (ii) s...

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  19. Examine f:R rarr [-1,1],f(x) = sin x functions if it is (i) injectiv...

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  20. Examine f:R+ rarr R +, f(x) =x +1/x "where"R+={x in R :x gt 0} functi...

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