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A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?
- a)If a relation S is transitive and circular, then S is an equivalence relation.
- b)If a relation S is reflexive and symmetric, then S is an equivalence relation.
- c)if a relation S is reflexive and circular, then S is an equivalence relation.
- d)if a relation S is circular and symmetric, then S is an equivalence relation.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A relation R is said to be circular if aRb and bRc together imply cRa....
Let's start with Option 3;
Option 3:if a relation S is reflexive and circular, then S is an equivalence relation.
It is correct.
- S is reflexive and circular; see that if are able to derive Symmetric and transitive property from these given properties.
aRa ∈ S and aRb ∈ S => bRa ∈ S //Using Reflexive and circular
aRb and bRa both exist then the relation is Symmetric.
- Now
aRb and bRc together => cRa and according to symmetricity ≡ aRc
aRb and bRc together => aRc
Hence Transitivity satisfied.
Hence S is an Equivalence Relation.
Example : S = { {a,a) (b.b) (c,c) } (diagonal relation)
It is correct.
- S is reflexive and circular; see that if are able to derive Symmetric and transitive property from these given properties.
aRa ∈ S and aRb ∈ S => bRa ∈ S //Using Reflexive and circular
aRb and bRa both exist then the relation is Symmetric.
- Now
aRb and bRc together => cRa and according to symmetricity ≡ aRc
aRb and bRc together => aRc
Hence Transitivity satisfied.
Hence S is an Equivalence Relation.
Example : S = { {a,a) (b.b) (c,c) } (diagonal relation)
Option 1: If a relation S is transitive and circular, then S is an equivalence relation.
It is not correct.
Consider a example of empty relation or S = {(a,b)}; it is transitive and circular but its not Equivalence Relation.
Hence S is not an equivalence Relation.
It is not correct.
Consider a example of empty relation or S = {(a,b)}; it is transitive and circular but its not Equivalence Relation.
Hence S is not an equivalence Relation.
Option 2: If a relation S is reflexive and symmetric, then S is an equivalence relation.
It is not correct. For a Relation S to be Equivalence Reflexive, Symmetric and Transitive are required.
It is not correct. For a Relation S to be Equivalence Reflexive, Symmetric and Transitive are required.
Option 4: if a relation S is circular and symmetric, then S is an equivalence relation.
It is not correct.
Consider a example of empty relation or S = {(a,b) , (b,a), (a,a)}; It is circular and symmetric but its not Equivalence relation.
Hence S is not an equivalence Relation.
It is not correct.
Consider a example of empty relation or S = {(a,b) , (b,a), (a,a)}; It is circular and symmetric but its not Equivalence relation.
Hence S is not an equivalence Relation.
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A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer?
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A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer?.
A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer?.
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A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?a)If a relation S is transitive and circular, then S is an equivalence relation.b)If a relation S is reflexive and symmetric, then S is an equivalence relation.c)if a relation S is reflexive and circular, then S is an equivalence relation.d)if a relation S is circular and symmetric, then S is an equivalence relation.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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