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Show that the relation is parallel to on the set S of all straight lines in a plane is an equivalence relation.

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What is an equivalence relation? Show that the relation of'similarity' on the set S of all triangle in a plane is an equivalence relation.

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Show that the relation R on the set Z of integers,given by R={(a,b):2 divides a-b}, is an equivalence relation.

Prove that the relation congruence modulo m on the set Z of all integers is an equivalence relation.

Show that the relation R on the set A{x in Z;0<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Illustrative Example
  1. Consider that the set A = {a, b, c}. Give an example of a relation R o...

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  2. Let R be the relation of the set Z of all integers defined by : R = ...

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  3. Show that the relation is parallel to on the set S of all straight lin...

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  4. Prove that the relation R on Z defined by (a ,\ b) in RhArr a-b is di...

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  5. Let n be a positive integer. Prove that the relation R on the set Z of...

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  6. Prove that a relation R defined on NxxN where (a, b)R(c, d) <=> ad = ...

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  7. Which of the following graphs represent the function of x ? Why

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  8. Let N be the set of natural numbers and the relation R be defined on ...

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  9. Which of the following relations are functions? Give reason. If it is ...

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  10. Let N be the set of natural numbers. Define a real valued function ...

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  11. Let f = {(1, 2), (2, 3), (0, 1), ( 1, 3)}be a linear function from...

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  12. Let A = {1,2,3},B={4,5} and let f={(1,4),(2,5),(3,5)}. Show that 'f' i...

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  13. Let N rarr N be defined by f(x) = 3x. Show that 'f' is not an onto fun...

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  14. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

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  15. If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

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  16. If f is a real function defined by f(x)=(x-1)/(x+1), then prove that f...

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  17. If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , p...

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  18. If f(x)=loge((1-x)/(1+x)); prove that f(a)+f(b)=f((a+b)/(1+a b))

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  19. माना f:R rarr R एक फलन इस प्रकार परिभाषित है, कि f(x)={:{(3x-1, " ...

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  20. For the relation y= + sqrtx, say whether it is a function or not. If i...

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