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Show that the relation R defined by R = ...

Show that the relation R defined by `R = {(a, b) (a - b)`, is divisible by 5, `a, b in N} is an equivalence relation.

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Show that the relation R defined by R = {(a, b): (a - b) is divisible by 3., a, b in N} is an equivalence relation.

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Show that the relation R defined by : R = (a,b) : a-b is divisible by 3 a,b in N is an equivalence relation.

If R is a relation in N xx N , show that the relation R defined by (a, b) R (c, d) if and only if ad = bc is an equivalence relation.

Show that relation R in Z of integers given by R = {x,y} : x - y is divisible by 5, x , y inZ } is an equivalence relation.

Let Z be the set of all integers and R be the relation on Z defined as R = (a,b) : a,b in Z and a-b is divisible by 5) Prove that R is an equivalence relation.

Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} is an equivalence relation.

Show that the relation R defined by (a, b) R(c,d)implies a+d=b+c in the set N is an equivalence relation.

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BETTER CHOICE PUBLICATION-RELATIONS AND FUNCTIONS -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. Prove that the relation R in Z of integers given by: R = {(x, y): 2x -...

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  2. Prove that the relation R in Z of integers given by: R = {(x, y): 3x -...

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  3. Show that the relation R defined by R = {(a, b) (a - b), is divisible ...

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  4. Check the injectivity and surjectivity of the following function: f ...

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  5. Check the injectivity and surjectivity of the following function: f :...

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  6. If f(x) =x/(x-1) then show that (fof)(x) = x.

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  7. If f:(1,3,4} rarr {1, 2,5} and g:(1,2,5) {1,3} be given by f = {(1, 2)...

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  8. If f : R rarr R defined by : f(x) = frac {3-2x}{4} is an inversible fu...

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  9. If f : R rarr R defined by : f(x) = frac {6-5x}{7} is an inversible fu...

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  10. Prove that the relation R in Z of integers given by: R = {(x, y): 2x -...

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  11. Let f:NrarrY, be a function defined as f(x) = 4x+3, where, Y = {y in ...

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  12. In a binary operation **: phi xx phi rarr phi is defined as a ** b = (...

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  13. If f(x) = 4x – 1 and g(x)=x^3 + 2, find gof

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  14. If f(x) = 4x – 1 and g(x)=x^3 + 2, find gof

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  15. If f(x) = sin x and g(x) = 2x, find fog.

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  16. Is f(x) = (x-1)/(x+1) invertible in its domain ? If so find, f^(-1) F...

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  17. Consider f:R^(+) rarr [-5, oo] given by f (x) = 9x^(2) + 6x - 5 show ...

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  18. If a**b=a/2+b/3 then find value of 2 ** 3.

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  19. Show that the relation R in the set R of real number defined as R = {(...

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  20. If R is the relation ‘lessthan from A={1,2,3,4,5} to B={1,4,5}. Write ...

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