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Congruence modulo 3 relation partitions ...

Congruence modulo 3 relation partitions the set Z into how many equivalence classes ?

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The relation congruence modulo 3 on the set `Z` partitions `Z` into three equivalence classes.
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MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. Write the smallest equivalence relation on A = {1,2,3}.

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  2. Congruence modulo 3 relation partitions the set Z into how many equiva...

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  3. Given an example of a relation which is reflexive, symmetric but not...

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  4. Given an example of a relation which is reflexive, transitive but n...

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  5. Given an example of a relation which is reflexive but neither symmet...

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  6. Find the least positive integer r such that -375 in [r]11

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  7. Find three positive integers x(i),i = I, 2, 3 satisfying 3x = 2 (mod 7...

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  8. State the reason for the relation R in the set {1, 2, 3} given by R ={...

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  9. Show that f : R to R defined as f(x) = sgn(x) is neither one-one nor o...

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  10. Give an example of a function which is injective but not surjective.

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  11. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  12. Express each of the following function as the sum of an even function ...

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  13. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  14. If the invertible function f is defined as f(X) = (3x-4)/5 , write f^(...

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  15. Let f , R to R and g , R to R defined as f(x) = | x |, g(x) = | 5x - 2...

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  16. Let * is a binary operation defined by a * b = 3a + 4b - 2, find 4*5.

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  17. Let the binary operation on Q defined as a * b = 2a + b - ab, find 3*4...

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  18. Let * is a binary operation on Z defined as a * b = a + b - 5 find the...

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  19. Find the number of binary operations on the set {a, b}.

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  20. Let * is a binary operation on [0, ¥) defined as a * b = sqrt (a^(2)+b...

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