Consider the following relations R=\(x, y) x, y are real numbers and x=w y 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 m. Then

(C) S is an equivalence relation but R is not an equivalence relation

(A) R is an equivalence relation but S is not an equivalence relation

(B) Neither R nor S is an equivalence relation

(D) R and S both are equivalence relations

Sets, Relations and Functions: JEE Main 2010 Mathematics question

JEE Main 2010 · Annual, Paper 1 · Q5371

JEE Main 2010Annual, Paper 1MathematicsHardSets, Relations and Functions168× since 2002

Consider the following relations

R=\{(x, y) \mid x, y

are real numbers and

x=w y

for some rational number

w\}

;

S=\left\{\left(\frac{m}{n}, \frac{p}{q}\right) \mid m, n, p\right.

and

q

are integers such that

n, q \neq 0

and

q m=p m\}

. Then