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Show that the relation R on the set A={1...

Show that the relation `R` on the set `A={1,\ 2,\ 3,\ 4,\ 5}` , given by `R={(a ,\ b):|a-b|` is even }, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But, no element of {1, 3, 5} is related to any element of {2, 4}.

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
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  3. Show that the relation R on the set A={1,\ 2,\ 3,\ 4,\ 5} , given by R...

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  4. Show that each of the relation R in the set A={x in Z: 0 le xle12},giv...

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  5. Give an example of a relation which is symmetric but neither reflex...

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  6. Show that the relation R. in the set A of all points in a place given ...

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  7. Show that the relation R. defined in the set A of all triangle as R={(...

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  8. Show that the relation R defined in the set A of all polygons as R=...

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  9. Let L be the set of all line in XY place and R be the relation in L de...

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  10. Let R be the relation in the set {1,2,3,4,} given by R = {(1,2),(2,2)...

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  11. Let R be the relation in the set N given by R={(a,b):a=b -2,b gt 6} c...

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  12. Let A be the set of all 50 students of class X in a school. Let f : A...

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  13. The function f:NtoN given by f(x)=2x

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  14. Prove that the function f: R rarr R given by f(x)=2 x is one-one and o...

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  15. Show that the function f: N rarr N, given by f(1)=f(2)=1 and f(x)=x-1,...

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  16. Check the injective and surjective of the following functions : f : R ...

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  17. Show that f : N rarr N given by f(x) = { ((x +1), if x is odd), ((x ...

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  18. Check the injectivity and surjectivity of the following functions f:...

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  19. Prove that the greatest integer function f : R rarrR given by f(x) =[x...

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  20. Show that the modulus function f: R rarr R given by f(x) = |x|, is nei...

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