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Consider the following relations: R = {(...

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; `S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"}` . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

A

R is an equivalence relation but S is not an equialence realtion

B

neither R nor S is an equivalence relation

C

S is an equivalene relation but R is not a equivalence relation

D

R and S both are equivalence relations.

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Consider the following relations: R = {(x, y) | x, y are real numbers ...

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  2. Which one of the following graph represents the function of x? Why?

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  3. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be onto...

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  4. Let A be the set of all 50 students of class XII in a school. Let f: A...

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  5. Prove that the function f : RrarrR given by f (x) = 2x is one-one and...

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  6. Show that the function: f: N rarr N given by f(1) = f (2) = 1 and f (x...

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  7. Show that function f: Rrarr R given by f(x) = x^2 is neither one-one n...

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  8. Show that f : NrarrN , given by : f(x) = {(x+1,,if x is odd,,),(x-1,,i...

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  9. If f : R rarr R is defined by f(x) = x + 2, find f(f(x))

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  10. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

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  11. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find fog

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  12. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find gof.

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  13. Find gof and fog, if f(x) = |x| and g(x) = |5x -2|

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  14. Let f(x) = (4x+3)/(6x-4), x ne 2/3 .show that fof (x) = x.

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  15. Find gof and fog if f: RrarrR and g: R rarr R are given by f(x) = co...

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  16. If the function f : R rarr R given by f(x) = x^2 +2 and g RrarrR be g...

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  17. Let f : { 1, 2, 3} rarr {a, b, c} be one-one and onto function given b...

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  18. Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by ...

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  19. Let Y = {n^2 : n in N} sub N Consider f : N rarr Y as f (n) = n^2 Show...

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  20. Let f: Nrar R be a function defined as : f(x) = 4x^2 + 12 x + 15. Sho...

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  21. Let f : N rarr N be a function deifned by f(x) = 9x^2 + 6x - 5. Show ...

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