Set, Relation and FunctionHard
Question
Consider the following relations:
R = {(x, y) | x, y are real numbers and x = wy for some rational number w};
S =
m, n, p and q are integers such that n, q ≠ 0 and qm = pn
. Then
R = {(x, y) | x, y are real numbers and x = wy for some rational number w};
S =
m, n, p and q are integers such that n, q ≠ 0 and qm = pn. ThenOptions
A.neither R nor S is an equivalence relation
B.S is an equivalence relation but R is not an equivalence relation
C.R and S both are equivalence relations
D.R is an equivalence relation but S is not an equivalence relation
Solution
xRy need not implies yRx
S:
⇔ qm = pn
reflexive
⇒ qm = pn, ps = rq ⇒ ms = rn transitive.
S is an equivalence relation.
S:
⇔ qm = pn reflexive ⇒ qm = pn, ps = rq ⇒ ms = rn transitive.S is an equivalence relation.
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