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Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is
  • a)
    symmetric but not transitive
  • b)
    partial order
  • c)
    equivalence relation
  • d)
    anti symmetric and not transitive
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let R be a relation "(x -y) is divisible by m", where x, y, ...
a) Since x - x = 0, m
=> x - x is divisible by m
(x,x) ∈ R
=> R is reflexive
b) Let (x,y) ∈ R
=> x - y = mq for some q ∈ I
=> y - x = m(-q)
y - x is divisible by m
(y,x) ∈ R
=> R is symmetric.
c) Let (x,y) and (y,z) ∈ R
=> x - y is divisible by m and y - z is divisible by m
=> x - y = mq and y - z = mq' for some q, q' ∈ I
=>(x-y)+(y-z) = m(q+q')
=> x - z = m(q + q'), q + q' ∈ I
(x,z) ∈ R
=> R is transitive.
Hence the relation is equivalence relation.
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Most Upvoted Answer
Let R be a relation "(x -y) is divisible by m", where x, y, ...
a) Since x - x = 0, m
=> x - x is divisible by m
(x,x) ∈ R
=> R is reflexive
b) Let (x,y) ∈ R
=> x - y = mq for some q ∈ I
=> y - x = m(-q)
y - x is divisible by m
(y,x) ∈ R
=> R is symmetric.
c) Let (x,y) and (y,z) ∈ R
=> x - y is divisible by m and y - z is divisible by m
=> x - y = mq and y - z = mq' for some q, q' ∈ I
=>(x-y)+(y-z) = m(q+q')
=> x - z = m(q + q'), q + q' ∈ I
(x,z) ∈ R
=> R is transitive.
Hence the relation is equivalence relation.
Free Test
Community Answer
Let R be a relation "(x -y) is divisible by m", where x, y, ...
a) Since x - x = 0, m
=> x - x is divisible by m
(x,x) ∈ R
=> R is reflexive
b) Let (x,y) ∈ R
=> x - y = mq for some q ∈ I
=> y - x = m(-q)
y - x is divisible by m
(y,x) ∈ R
=> R is symmetric.
c) Let (x,y) and (y,z) ∈ R
=> x - y is divisible by m and y - z is divisible by m
=> x - y = mq and y - z = mq' for some q, q' ∈ I
=>(x-y)+(y-z) = m(q+q')
=> x - z = m(q + q'), q + q' ∈ I
(x,z) ∈ R
=> R is transitive.
Hence the relation is equivalence relation.
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Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R isa)symmetric but not transitiveb)partial orderc)equivalence relationd)anti symmetric and not transitiveCorrect answer is option 'C'. Can you explain this answer?
Question Description
Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R isa)symmetric but not transitiveb)partial orderc)equivalence relationd)anti symmetric and not transitiveCorrect answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R isa)symmetric but not transitiveb)partial orderc)equivalence relationd)anti symmetric and not transitiveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R isa)symmetric but not transitiveb)partial orderc)equivalence relationd)anti symmetric and not transitiveCorrect answer is option 'C'. Can you explain this answer?.
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