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Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w};   and q are integers such that n, q ≠ 0 and qm = pn}.Then                                   [2010]
  • 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
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the following relations: R = {(x, y) | x, y are real numbers ...
x Ry need not implies yRx ∴ R is not symmetric and hence not an equivalence relation
Given qm = pn  
 qm = pn, ps= rq
⇒ ms = rn (transitive).
S is an equivalence relation.
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Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w};and q are integers such that n, q ≠ 0 and qm = pn}.Then [2010]a)Neither R nor S is an equivalence relationb)S is an equivalence relation but R is not an equivalence relationc)R and S both are equivalence relationsd)R is an equivalence relation but S is not an equivalence relationCorrect answer is option 'B'. Can you explain this answer?
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Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w};and q are integers such that n, q ≠ 0 and qm = pn}.Then [2010]a)Neither R nor S is an equivalence relationb)S is an equivalence relation but R is not an equivalence relationc)R and S both are equivalence relationsd)R is an equivalence relation but S is not an equivalence relationCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w};and q are integers such that n, q ≠ 0 and qm = pn}.Then [2010]a)Neither R nor S is an equivalence relationb)S is an equivalence relation but R is not an equivalence relationc)R and S both are equivalence relationsd)R is an equivalence relation but S is not an equivalence relationCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w};and q are integers such that n, q ≠ 0 and qm = pn}.Then [2010]a)Neither R nor S is an equivalence relationb)S is an equivalence relation but R is not an equivalence relationc)R and S both are equivalence relationsd)R is an equivalence relation but S is not an equivalence relationCorrect answer is option 'B'. Can you explain this answer?.
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