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Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.
Choose the correct answer:
Choose the correct answer:
- a)R is reflexive and symmetric but not transitive
- b)R is reflexive and transitive but not symmetric
- c)R is symmetric and transitive but not reflexive
- d)R is an equivalence relation
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6...
Let R be the relation in the set {1, 2,3, 4} is given by:
R = {(5,6), (6,6), (5,5), (8,8), (5,7), (7,7), (7,6)}
(a) (5,5), (6,6), (7,7), (8,8) ∈ R Therefore, R is reflexive.
(b) (5,6) ∈ R but (6,5) ∈ R. Therefore, R is not symmetric.
(c) If (5, 7) ∈ R and (7, 6) ∈ R then (5, 6) ∈ R. Therefore, R is transitive.
R = {(5,6), (6,6), (5,5), (8,8), (5,7), (7,7), (7,6)}
(a) (5,5), (6,6), (7,7), (8,8) ∈ R Therefore, R is reflexive.
(b) (5,6) ∈ R but (6,5) ∈ R. Therefore, R is not symmetric.
(c) If (5, 7) ∈ R and (7, 6) ∈ R then (5, 6) ∈ R. Therefore, R is transitive.
Most Upvoted Answer
Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6...
Explanation:
Relation R: R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}
Reflexive: R is reflexive if (a, a) ∈ R for every a ∈ A, where A is the set of all elements of R. In this case, (5, 5), (6, 6), and (8, 8) are the only elements in R that satisfy this condition. Therefore, R is not reflexive.
Symmetric: R is symmetric if (a, b) ∈ R implies (b, a) ∈ R for every a, b ∈ A. In this case, (5, 6) and (7, 6) are the only elements in R that do not have a corresponding (b, a) pair. Therefore, R is not symmetric.
Transitive: R is transitive if (a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R for every a, b, c ∈ A. In this case, (5, 6) and (6, 6) are both in R, but (5, 6) and (6, 7) are not in R. Therefore, R is not transitive.
Equivalence Relation: An equivalence relation is reflexive, symmetric, and transitive. Since R is not reflexive, symmetric, or transitive, it is not an equivalence relation.
Therefore, the correct answer is option B: R is reflexive and transitive but not symmetric.
Relation R: R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}
Reflexive: R is reflexive if (a, a) ∈ R for every a ∈ A, where A is the set of all elements of R. In this case, (5, 5), (6, 6), and (8, 8) are the only elements in R that satisfy this condition. Therefore, R is not reflexive.
Symmetric: R is symmetric if (a, b) ∈ R implies (b, a) ∈ R for every a, b ∈ A. In this case, (5, 6) and (7, 6) are the only elements in R that do not have a corresponding (b, a) pair. Therefore, R is not symmetric.
Transitive: R is transitive if (a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R for every a, b, c ∈ A. In this case, (5, 6) and (6, 6) are both in R, but (5, 6) and (6, 7) are not in R. Therefore, R is not transitive.
Equivalence Relation: An equivalence relation is reflexive, symmetric, and transitive. Since R is not reflexive, symmetric, or transitive, it is not an equivalence relation.
Therefore, the correct answer is option B: R is reflexive and transitive but not symmetric.
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Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer?
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Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer?.
Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Let R be the relation in the set {5, 6, 7, 8} given by R = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}.Choose the correct answer:a)R is reflexive and symmetric but not transitiveb)R is reflexive and transitive but not symmetricc)R is symmetric and transitive but not reflexived)R is an equivalence relationCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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