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For the given relation R on a set S, det...

For the given relation R on a set S, determine which are equivalence relations : (i) S is the set of all rational numbers a R b iff a= b. (ii) S is the set of all real numbers iff : (I) `|a |= |b|` (II) `a ge b`.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. The following figure shows a relation between P and Q. Write the relat...

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  2. For the given relation R on a set S, determine which are equivalence r...

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  3. For the given relation R on a set S, determine which are equivalence r...

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  4. If R is the relation in N xx N defined by (a, b) R (c,d) if and only i...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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