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Relation R on Z defined as R = {(x ,y): ...

Relation R on Z defined as `R = {(x ,y): x - y "is an integer"}`. Show that R is an equivalence relation.

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R is an equivalence relation
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SUBHASH PUBLICATION-RELATIONS AND FUNCTIONS -THREE MARKS QUESTIONS WITH ANSWERS
  1. Verify whether the function f : A to B , where A = R - {3} and B = R -...

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  2. If * is a binary operation defined on A = N xx N by (a , b) ** (c, d) ...

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  3. Show that the relation R in the set of all integers, Z defined by R = ...

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  4. Show that the relation R in the set of all natural number, N defined b...

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  5. Show that the relation R in the set A = {x in Z : 0 le x le 12} given ...

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  6. Let R be relation on the set A = {1,2,3,.....,14} by R = {(x,y):3x - y...

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  7. Relation R on Z defined as R = {(x ,y): x - y "is an integer"}. Show t...

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  8. Show that the relation R in R defined R = {(a, b) : a le b} is reflexi...

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  9. Show that if f : R - {7/5} to R - {3/5} is defined by f(x) = (3x + 4)/...

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  10. Show that if f : A to B and g: B to C are one-one, then gof: A to C is...

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  11. Show that if f: A to B and g: B to C are onto, then gof : A to C is al...

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  12. Consider f: N to N, g : N to N and h: N to R defined as f(x) = 2x, g(y...

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  13. If f: X to Y, g : Y to Z and h: Z to S are functions, then ho(gof) = (...

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  14. Let f: X to Y and g: Y to Z be two invertible functions. Then gof is ...

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  15. If R(1) and R(2) are equivalence relations in a set A, show that R(1) ...

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  16. Prove that the relation R defined on the set of real numbers R as R = ...

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