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Let S denote set of all integers. Define a relation R on S as 'aRb if ab ≥ 0 where a, b ∈ S. Then R is :
  • a)
    Reflexive but neither symmetric nor transitive relation
  • b)
    Reflexive, symmetric but not transitive relation
  • c)
    An equivalence relation
  • d)
    Symmetric but neither reflexive nor transitive relation ​
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let S denote set of all integers. Define a relation R on S as 'aRb...
S = Set of all integers and
R = {(a, b), a , b ∈ S and a b≥ 0 }
For reflexive: aRa ⇒ a.a = a2 ⇒ 0
for all integers a. a ≥ 0
For symmetric : aRb ⇒ ab ⇒ 0 a, b ∈ S
If ab > 0, then ba ≥ 0 ⇒ bRa
For transitive:
If ab≥ 0 , be≥ 0, then also ac≥ 0
Rlation R is reflexive, symmetric and transitive.
Therefore relation is equivalence.
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Most Upvoted Answer
Let S denote set of all integers. Define a relation R on S as 'aRb...
The relation R on S is defined as aRb if ab < 0.="" />
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Let S denote set of all integers. Define a relation R on S as 'aRb if ab ≥ 0 where a, b ∈ S. Then R is :a)Reflexive but neither symmetric nor transitive relationb)Reflexive, symmetric but not transitive relationc)An equivalence relationd)Symmetric but neither reflexive nor transitive relation ​Correct answer is option 'C'. Can you explain this answer?
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Let S denote set of all integers. Define a relation R on S as 'aRb if ab ≥ 0 where a, b ∈ S. Then R is :a)Reflexive but neither symmetric nor transitive relationb)Reflexive, symmetric but not transitive relationc)An equivalence relationd)Symmetric but neither reflexive nor transitive relation ​Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let S denote set of all integers. Define a relation R on S as 'aRb if ab ≥ 0 where a, b ∈ S. Then R is :a)Reflexive but neither symmetric nor transitive relationb)Reflexive, symmetric but not transitive relationc)An equivalence relationd)Symmetric but neither reflexive nor transitive relation ​Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let S denote set of all integers. Define a relation R on S as 'aRb if ab ≥ 0 where a, b ∈ S. Then R is :a)Reflexive but neither symmetric nor transitive relationb)Reflexive, symmetric but not transitive relationc)An equivalence relationd)Symmetric but neither reflexive nor transitive relation ​Correct answer is option 'C'. Can you explain this answer?.
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