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For real numbers x and y, define x R y i...

For real numbers x and y, define x R y if and only if `x-y +sqrt(2)` is an irrational number. Is R transitive? Explain your answer.

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MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. Find least non negative integer r such that 7xx13xx23xx413 -= r "(mod ...

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

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  3. For real numbers x and y, define x R y if and only if x-y +sqrt(2) is ...

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  4. Let A = {a,b,c) and the relation R be defined on A as follows: R={{a...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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