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Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let...

Let `X = {1, 2, 3, 4, 5, 6, 7, 8, 9}`. Let `R_1` be a relation in X given by `R_1 = {(x, y) : x – y` is divisible by 3}` and `R_2` be another relation on X given by `R_2 = {(x, y): {x, y} sub {1, 4, 7}` or `{x, y} sub {2, 5, 8}` or `{(x, y} sub {3, 6, 9}`. Show that `R_1 = R_2`.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let R and S be two non-void relations on a set A. Which of the followi...

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  2. Let R1 and R2 be two relations defined on a non-empty set A. Which of ...

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  3. Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let R1 be a relation in X given ...

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  4. Let A = {1,2,3}. Then show that the nmber of relations (1,2) and (2,3)...

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  5. Which of the following relations are functions form A = (1,3,5,7,9) to...

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  6. Which of the following are the functions of RNA?

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  7. Which of the following functions are odd or even or neither : f(x)=|...

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  8. Which of the following are the functions of RNA?

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  9. Which of the following functions are not derivable at x=0?

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  10. Correct the following statement , "Every function is a relation is a r...

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  11. Give an example of a function which is one-one but not onto

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  12. Give an example of a function which is one-one but not onto

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  13. Give an example of a function which is one-one but not onto

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  14. If X = {a,b,c,d} and Y = {f,b,d,g}, find X-Y and Y-X.

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  15. Let x = (a,b,c) and Y = (0,1,2,3,4,5), define a one-one function from ...

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  16. Prove that the function f:N rarrN defined by f(x)=x^2 +x+ 1 is one -on...

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  17. Let f, X rarr Y be defined by f(x) = x^2 +1, for all x in X where X =...

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  18. Which of the following functions are one-one? f(x) = 3x + 2

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  19. Which of the following functions are one-one? f(x) = 2x^2 + 3

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  20. Which of the following functions are one-one? f(x) = (1)/(3x-4)

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