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Show that the relation ‘is perpendicular...

Show that the relation ‘is perpendicular to' on the set A of all coplanar straight lines is symmetric but it is neither reflexive nor transitive.

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The relation ‘is parallel to’, on the set A of all coplanar straight lines is an equivalence relation.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. Determine the domain and range of the following relation : {(x,y): y =...

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  2. Let A = {1, 2, 3, 4} and B = {x,y,z}. Let R be a relation from A into ...

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  3. Show that the relation ‘is perpendicular to' on the set A of all copla...

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  4. Show that R= {(a, b): a ge b} is reflexive and transitive but not sym...

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  5. Show that the relation ‘is a factor of’ on the set N of all natural nu...

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  6. Let A = {1, 2, 3, .........., 14}. Define a relation R from A to A by ...

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  7. Define a relation R on the set N of natural numbers by : R= {(x, y): y...

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  8. LetA= {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): ...

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  9. LetA= {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): ...

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  10. LetA= {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): ...

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  11. The following figure shows a relation between P and Q. Write the relat...

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  12. The following figure shows a relation between P and Q. Write the relat...

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

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

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

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

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

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

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

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

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