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Let A = (1,2,3,……….,9) and R be the rela...

Let A = (1,2,3,……….,9) and R be the relation in `AxxA` defined by (a,b) R (c,d) if: a+d=b+c for (a,b), (c,d) in `AxxA`. Prove that R is an equivalence relation. Also obtain the equivalence class {(2,5)}

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Show that the function f : R rarr R defined by : f(x) = x/(x^2+1) AA ...

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

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

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

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

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

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

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

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

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

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

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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 defined on R by a*b = 1 + ab AA a,binR...

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

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

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

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  18. Let f : X rarr Y be an function. Define a relation R in X given by : R...

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  19. If R1 and R2 are equivalence relations in a set A, show that R1 nn R...

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  20. Show that the number of equivalence relation in the set {1, 2, 3} cont...

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