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Given the relation R = {(1, 2), (2, 3)} ...

Given the relation R = {(1, 2), (2, 3)} on the set of natural numbers, add a minimum of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. If R is the relation in N xx N defined by (a, b) R (c,d) if and only i...

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  2. Is inclusion of a subset in another, in the context of a universal set...

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  3. Given the relation R = {(1, 2), (2, 3)} on the set of natural numbers,...

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  4. Let f(x) = x^2 and g(x) = 2x + 1 be two real functions. Find : (f + g...

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  5. Let f(x)= sqrtx and g (x) = x be two functions defined over the set of...

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  6. If f and g are functions defined by : f(x)= sqrt(x-1), g(x)=1/x,then d...

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  7. If f and g are functions defined by : f(x)= sqrt(x-1), g(x)=1/x,then d...

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  8. If f and g are functions defined by : f(x)= sqrt(x-1), g(x)=1/x,then d...

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  9. If f and g are functions defined by : f(x)= sqrt(x-1), g(x)=1/x,then d...

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  10. Define the real valued function f:R- {0} rarr R defined by f(x) = 1/x,...

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  11. Sketch the graph of the following function : f(x)= 4- 2x. Also find...

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  12. Sketch the graph of the following function : (i) f(x)=|x+2| (ii) f(x)...

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  13. Draw the graph of f(x) = sgn (x -2).

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  14. Draw the graph of y = [x] + x.

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  15. Draw the graph of the function : f(x)= {(0 if x is an even i nteg er)...

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  16. Let R be a relation from Q to Q defined by : R = {(a, b): a,b in Q and...

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  17. Let R be a relation from Q to Q defined by : R = {(a, b): a,b in Q and...

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  18. Let R be a relation from Q to Q defined by : R = {(a, b): a,b in Q and...

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  19. Let R be a relation from N to N defined by : R = {(a, b): a, b in N an...

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  20. Let R be a relation from N to N defined by R = {(a, b) : a, b in N and...

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