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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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JMD PUBLICATION-RELATION & FUNCTIONS-EXERCISE
  1. If f(x)=abs(x) and g(x)= [x] thenf@g(-1/2) is

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  2. If f:R–>R is defined and f(x)= (3x+4)/2 then f^(-1) is

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  3. If f: Rrarr R given by f(x) = (x^3) + 3, then f^-1(x) equals·:

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  4. If f(x) =(x^2), then f@ f(x) =

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  5. If f(x) =2x-3, then f^(-1)(x) =

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  6. The smallest equivalence relation R on set A ={1,2,8} is=

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  7. The range of(abs(x-1))/(x-1) is 1

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  8. If f(x)=4x-5 then f^-1 (x)=(x+5)/4

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  9. If f(x)= [x], g (x) = abs(x), then find the value of (fog) (5/2) - (go...

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  10. If f:N–>N is defined by{[(n+1)/2 (if n is odd) ] ,[( n/2)(if n is even...

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  11. Prove that function f: RrarrR, f (x) = (3-2x)/7- is one-one and onto. ...

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  12. Show that the relation R={(a,b):aleb} is not equivalence relation

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  13. Let T be the set of all triangles in a plane with R as a relation in T...

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  14. Let f: R–>R is defined as f(x)=x^2 is neither one one nor onto

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  15. Let f:R-{-3/5}–>R be a function defined as f(x)= (2x)/(5x+3) find f^(-...

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  16. If R={(x,y):x+2y=8} is a relation on N write the range of R

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  17. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

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  18. Let A=R-{3} and B=R-{1} . Consider the function f:A–>B. defined by f(x...

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

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  20. If f(x)=(4x+3)/(6x-4) ,x != 2/3 show that f@f(x) =x for all x != 2/3....

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