DSSSB TGT/PGT/PRT Exam  >  DSSSB TGT/PGT/PRT Questions  >  Let S denote set of all integers. Define a re... Start Learning for Free
Let S denote set of all integers. Define a relation R on S as ‘aRb if ab ≥ 0 where a, b ϵ 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 ‘a...
S= Set of all integers and
R= {(a, b) , a , b ∈ S and ab ≥ 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, bc ≥ 0, then also ac ≥ 0
Relation R is reflexive, symmetric and transitive.
Therefore relation is equivalence.
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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 relationCorrect 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 relationCorrect answer is option 'C'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT 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 relationCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 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 relationCorrect answer is option 'C'. Can you explain this answer?.
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