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Let R be a sym m etric and transitive relation on a set A Then
  • a)
    R is reflexive and hence an equivalence relation
  • b)
    R is reflexive and hence a partial order
  • c)
    R is reflexive and hence not an equivalence relation
  • d)
    None of the above
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let R be a sym m etric and transitive relation on a set A Thena)R is r...
A relation which is symmetric and transitive, need not foe reflexive relation.
(i) R = {}; on the set A = {a, b}. The relation R is symmetric and transitive but not reflexive.
(ii) R = {(a, a), (b, b)}; on the set A = {a, b}.
The relation R is symmetric, transitive and also reflexive.
∴ A relation is transitive and symmetric relation but need not be reflexive relation.
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Let R be a sym m etric and transitive relation on a set A Thena)R is reflexive and hence an equivalence relationb)R is reflexive and hence a partial orderc)R is reflexive and hence not an equivalence relationd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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Let R be a sym m etric and transitive relation on a set A Thena)R is reflexive and hence an equivalence relationb)R is reflexive and hence a partial orderc)R is reflexive and hence not an equivalence relationd)None of the aboveCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let R be a sym m etric and transitive relation on a set A Thena)R is reflexive and hence an equivalence relationb)R is reflexive and hence a partial orderc)R is reflexive and hence not an equivalence relationd)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a sym m etric and transitive relation on a set A Thena)R is reflexive and hence an equivalence relationb)R is reflexive and hence a partial orderc)R is reflexive and hence not an equivalence relationd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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