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Consider the following relations: R = {(...

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; `S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"}` . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

A

is an equivalence relation but S is not an equivalence relation

B

neither R nor S is an equivalence relation

C

S is an equivalence relation but R is not an equivalence relation

D

R and S are both equivalence relations.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
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  3. Consider the following relations: R = {(x, y) | x, y are real numbers ...

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  4. Let S={1, 2, 3,4}. The total number of unordered pairs of disjoint sub...

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  5. The domain of the function f(x) = 1/(sqrt(|x|-x)) is :

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  6. Let P = {theta: sin theta- cos theta= sqrt2 cos theta} and Q= {theta: ...

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  7. Let f(x)=x^2a n dg(x)=sinx for all x in R Then the set of all x satis...

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  8. In a town of 10,000 families, it was found that 40% families buy newsp...

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  9. In a town of 10000 families, it was found that 40% families buy newspa...

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  10. In a town of 10000 families, it was found that 40% families buy newspa...

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  11. In a town of 10,000 families, it was found that 40% families buy newsp...

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  12. Given A = {x: pi/6 le x le pi/3} and f (x) = cos x -x(1 + x), find f (...

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  13. Prove that f (x) =x-[x], where [x] denotes the integral part of x not ...

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  14. Find the domain of the function f(x)= ([x]+1)/([x]-1), where [x] denot...

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  15. Find the domain of the following function : f(x)= 1/(sqrt(|x|-x)).

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  16. Find the domain of the following function : f(x)= sqrt(cos(sinx))+ s...

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  17. Find the domain of the following : f(x) = 1/(log10(1-x))+ sqrt (x+2)...

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  18. Find the domain and range of the following function : f(x) =1 /(sqrt...

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  19. Find the domain and range of the following function : f(x) = sin (lo...

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  20. Find the domain of definition of the function f (x) given by : f(x) = ...

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