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Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?
- a)R = {(7, 8), (8, 7), (8, 9)}
- b)R = {(7, 7), (8, 8), (9, 9)}
- c)R = {0}
- d)R = {(7, 8), (8, 8), (8, 9)}
Correct answer is option 'B'. Can you explain this answer?
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Which of the following relations is reflexive but not transitive for t...
The relation R= {(7, 7), (8, 8), (9, 9)} is reflexive as every element is related to itself i.e. (a,a) ∈ R, for every a∈A. and it is not transitive as it does not satisfy the condition that for a relation R in a set A if (a1, a2)∈R and (a2, a3)∈R implies that (a1, a3) ∈ R for every a1, a2, a3 ∈ R.
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Which of the following relations is reflexive but not transitive for t...
Reflexive Relation:
A relation R on a set T is reflexive if every element in T is related to itself. In other words, for every element a in T, (a, a) must be in R.
Transitive Relation:
A relation R on a set T is transitive if for every three elements a, b, and c in T, if (a, b) is in R and (b, c) is in R, then (a, c) must be in R.
Explanation:
To determine which relation is reflexive but not transitive for the set T = {7, 8, 9}, we need to check each relation based on the definitions of reflexive and transitive relations.
Relation a:
R = {(7, 8), (8, 7), (8, 9)}
- (7, 7) is not in R, so it is not reflexive.
- (7, 9) is not in R, so it is not transitive.
Relation b:
R = {(7, 7), (8, 8), (9, 9)}
- (7, 7), (8, 8), and (9, 9) are all in R, so it is reflexive.
- Since there are no other pairs in R, transitivity does not apply. Therefore, it is vacuously transitive.
Relation c:
R = {0}
- There are no pairs in R, so it is neither reflexive nor transitive.
Relation d:
R = {(7, 8), (8, 8), (8, 9)}
- (7, 7) is not in R, so it is not reflexive.
- (7, 9) is not in R, so it is not transitive.
Conclusion:
Based on the definitions of reflexive and transitive relations, the only relation that is reflexive but not transitive for the set T = {7, 8, 9} is relation b: R = {(7, 7), (8, 8), (9, 9)}. This is because it includes all elements related to themselves (reflexive), but there are no other pairs to check for transitivity.
A relation R on a set T is reflexive if every element in T is related to itself. In other words, for every element a in T, (a, a) must be in R.
Transitive Relation:
A relation R on a set T is transitive if for every three elements a, b, and c in T, if (a, b) is in R and (b, c) is in R, then (a, c) must be in R.
Explanation:
To determine which relation is reflexive but not transitive for the set T = {7, 8, 9}, we need to check each relation based on the definitions of reflexive and transitive relations.
Relation a:
R = {(7, 8), (8, 7), (8, 9)}
- (7, 7) is not in R, so it is not reflexive.
- (7, 9) is not in R, so it is not transitive.
Relation b:
R = {(7, 7), (8, 8), (9, 9)}
- (7, 7), (8, 8), and (9, 9) are all in R, so it is reflexive.
- Since there are no other pairs in R, transitivity does not apply. Therefore, it is vacuously transitive.
Relation c:
R = {0}
- There are no pairs in R, so it is neither reflexive nor transitive.
Relation d:
R = {(7, 8), (8, 8), (8, 9)}
- (7, 7) is not in R, so it is not reflexive.
- (7, 9) is not in R, so it is not transitive.
Conclusion:
Based on the definitions of reflexive and transitive relations, the only relation that is reflexive but not transitive for the set T = {7, 8, 9} is relation b: R = {(7, 7), (8, 8), (9, 9)}. This is because it includes all elements related to themselves (reflexive), but there are no other pairs to check for transitivity.
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Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'B'. Can you explain this answer?
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Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct 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 Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct 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 Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'B'. Can you explain this answer?.
Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct 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 Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct 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 Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'B'. Can you explain this answer?.
Solutions for Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?a)R = {(7, 8), (8, 7), (8, 9)}b)R = {(7, 7), (8, 8), (9, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct 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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