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Let S be a non empty symmetric and transitive binary operation on a non empty set A. Consider any pair (a, b) ε S. Since S is symmetric, (b, a) ε S. Further, since S is transitive, (a, b) ε S. Which one of the following statements is true?
  • a)
    S is reflexive relation since (a, b) ε S.
  • b)
    S is a reflexive relation since the reasoning holds for any pair of elements in S.
  • c)
    S is a reflexive relation since because the above reasoning is true only for the specific pair (a, a) ε S that has been considered.
  • d)
    S need not be reflexive because there, be other elements in A which are not related to any element in .4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let S be a non empty symmetric and transitive binary operation on a no...
Here, (a, b) ε S so (b, a) ε S.
Since S is transitive.
So, (a, a) ε S so it is reflexive.
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Most Upvoted Answer
Let S be a non empty symmetric and transitive binary operation on a no...
Since S is symmetric, if (a, b) is in S, then (b, a) must also be in S.

Since S is transitive, if (a, b) is in S and (b, c) is in S, then (a, c) must also be in S.

Now, let's consider the pair (a, b). Since S is symmetric, we know that (b, a) is also in S.

Since S is transitive, if (a, b) is in S and (b, a) is in S, then (a, a) must also be in S.

Therefore, for any pair (a, b), (a, a) must be in S.
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Community Answer
Let S be a non empty symmetric and transitive binary operation on a no...
Here, (a, b) ε S so (b, a) ε S.
Since S is transitive.
So, (a, a) ε S so it is reflexive.
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Let S be a non empty symmetric and transitive binary operation on a non empty set A. Consider any pair (a, b)ε S. Since S is symmetric, (b, a)ε S. Further, since S is transitive, (a, b)ε S. Which one of the following statements is true?a)S is reflexive relation since (a, b)εS.b)Sis a reflexive relation since the reasoning holds for any pair of elements in S.c)S is a reflexive relation since because the above reasoning is true only for the specific pair (a, a) εS that has been considered.d)S need not be reflexive because there, be other elements in A which are not related to any element in .4Correct answer is option 'C'. Can you explain this answer?
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Let S be a non empty symmetric and transitive binary operation on a non empty set A. Consider any pair (a, b)ε S. Since S is symmetric, (b, a)ε S. Further, since S is transitive, (a, b)ε S. Which one of the following statements is true?a)S is reflexive relation since (a, b)εS.b)Sis a reflexive relation since the reasoning holds for any pair of elements in S.c)S is a reflexive relation since because the above reasoning is true only for the specific pair (a, a) εS that has been considered.d)S need not be reflexive because there, be other elements in A which are not related to any element in .4Correct answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let S be a non empty symmetric and transitive binary operation on a non empty set A. Consider any pair (a, b)ε S. Since S is symmetric, (b, a)ε S. Further, since S is transitive, (a, b)ε S. Which one of the following statements is true?a)S is reflexive relation since (a, b)εS.b)Sis a reflexive relation since the reasoning holds for any pair of elements in S.c)S is a reflexive relation since because the above reasoning is true only for the specific pair (a, a) εS that has been considered.d)S need not be reflexive because there, be other elements in A which are not related to any element in .4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let S be a non empty symmetric and transitive binary operation on a non empty set A. Consider any pair (a, b)ε S. Since S is symmetric, (b, a)ε S. Further, since S is transitive, (a, b)ε S. Which one of the following statements is true?a)S is reflexive relation since (a, b)εS.b)Sis a reflexive relation since the reasoning holds for any pair of elements in S.c)S is a reflexive relation since because the above reasoning is true only for the specific pair (a, a) εS that has been considered.d)S need not be reflexive because there, be other elements in A which are not related to any element in .4Correct answer is option 'C'. Can you explain this answer?.
Solutions for Let S be a non empty symmetric and transitive binary operation on a non empty set A. Consider any pair (a, b)ε S. Since S is symmetric, (b, a)ε S. Further, since S is transitive, (a, b)ε S. Which one of the following statements is true?a)S is reflexive relation since (a, b)εS.b)Sis a reflexive relation since the reasoning holds for any pair of elements in S.c)S is a reflexive relation since because the above reasoning is true only for the specific pair (a, a) εS that has been considered.d)S need not be reflexive because there, be other elements in A which are not related to any element in .4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
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