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On the set N of all natural numbers, a r...

On the set N of all natural numbers, a relation R is defined as follows: `AA n,m in N`, n R m Each of the natural numbers n and m leaves the remainder less than 5.Show that R is an equivalence relation. Also, obtain the pairwise disjoint subsets determined by R.

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Let R be the quivalence relation in the set Z of integerx given by: R ...

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  2. If A = {1,2,3} and f,g are relations corresponding to the subset of A ...

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  3. On the set N of all natural numbers, a relation R is defined as follow...

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  4. Show that the function f : R rarr R defined by : f(x) = x/(x^2+1) AA ...

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  5. Let A = (0,1,2,3) and define a relation R on A as follows R = (0,0),(0...

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  6. Let A = (1,2,3,……….,9) and R be the relation in AxxA defined by (a,b) ...

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  7. If f = (5,2),(6,3), g = (2,5),(3,6), write fog.

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  8. Let f : R rarr R be defined by f(x) = x^2 +1 Find the pre-image of 17

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  9. Let f : R rarr R be defined by f(x) = x^2 +1 Find the pre-image of -3

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  10. let the function : f R rarr R to be defined by f(x) = cos x for all x ...

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  11. Let A = R - (3), B = R = (1). Let f: A rarr B be defined by: f(x) = (x...

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  12. Let '*' be the binary operation on Q. Find which of the following bina...

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  13. Let '*' be the binary operation on Q. Find which of the following bina...

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  14. Let '*' be the binary operation on Q. Find which of the following bina...

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  15. Let '*' be the binary operation on Q. Find which of the following bina...

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  16. Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR...

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  17. Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR...

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  18. Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR...

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  19. Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR...

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  20. Is the binary operation'*' defined on Z (set of integers) by m*n = m-n...

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