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Show that the relation R in the set of r...

Show that the relation R in the set of real numbers, defined as `R = {(a,b): a le b^(2) }` is neither reflexive nor symmetric nor transitive.

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MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. Let A = {a,b,c) and the relation R be defined on A as follows: R={{a...

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

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  3. Show that the relation R in the set of real numbers, defined as R = {(...

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  4. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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