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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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MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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  2. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

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  3. Let * is a binary operation on the set of all non-zero real numbers, g...

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  4. Test whether the relations are reflexive, symmetric or transitive on t...

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

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  6. If f:XtoY and g:YtoZ be two bijective functions, then prove that (gof)...

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  7. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

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  8. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

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  9. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

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  10. Examine f:(-1,1) rarr R,f(x) = x/(1-x^2functions if it is (i) injecti...

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  11. Consider f:R(+) [4, oo] is given by f(x)= x^(2) + 4. Show that f is in...

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  12. Test whether the relations are reflexive, symmetric or transitive on t...

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

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  14. Let A = {1, 2, 3). Then, show that the number of relations containing ...

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  15. Let R be a relation on the set A of ordered pairs of positive integers...

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  16. Show that f : N to N, given by f(x)= {(x+1", if x is odd"),(x-1", if...

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  17. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

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  18. Congruence modulo 3 relation partitions the set Z into how many equiva...

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

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  20. Constract the composition table/multiplication table for the binary op...

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