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

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 ne 0 " and "qm = pn`}. Then :

A

R 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 both are equivalence relations

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Knowledge Check

  • If p, q, r are real numbers then:

    A
    max. (p, q) `lt` max. (p, q, r)
    B
    min. `(p, q)=(1)/(2)(p+q-|p-q|)`
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    D
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    A
    ` p=1`
    B
    ` p=1 or 0`
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    `p=-2`
    D
    `p=-2 or 0`

  • If A.M. and G.M. of x and y are in the ration p : q, then x:y is :

    A
    `p-sqrt( p^(2) + q^(2) ) : p + sqrt( p ^(2) + q^(2))`
    B
    `p+sqrt( p^(2) + q^(2) ) : p - sqrt( p ^(2) + q^(2))`
    C
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