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.
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
Let A = {2, 3, 4, 5} and let R = {(2, 2), (3, 3), (4, 4), (5, 5), (2, 3), (3, 2), (3, 5), (5, 3)} be a relation in A. Th...If A, B, C are three sets, then A - (B ∪ C) is equal to :-...Given below are two statements:Statement I: The function $f:\mathbf{R} \rightarrow \mathbf{R}$ defined by $f(x) = \frac{...If f(x) = ax + b (a < 0) is an onto function defined as f : [0, 1] → [0, 2], then cot is equal to...If the graph of the function y = f(x) is continuous and passes through the point (5,2) then is equal to -...