Class 12 Exam > Class 12 Questions > Which of the following relations is reflexive...
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Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?
- a)R = {(7, 7), (8, 8), (9, 9)}
- b)R = {(7, 8), (8, 7), (8, 9)}
- c)R = {0}
- d)R = {(7, 8), (8, 8), (8, 9)}
Correct answer is option 'A'. Can you explain this answer?
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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 (a, b) and (b, c) in R, (a, c) is also in R. In other words, if there is a chain of two or more related elements, then the first and last elements must also be related.
Analysis of the given options:
Let's analyze each option to determine which one is reflexive but not transitive for the set T = {7, 8, 9}.
Option A (R = {(7, 7), (8, 8), (9, 9)}):
- This relation is reflexive because every element in T is related to itself.
- It is not transitive because there is no chain of related elements. For example, (7, 7) and (7, 7) are related, but (7, 7) and (7, 7) do not imply (7, 7) is related to (7, 7).
Option B (R = {(7, 8), (8, 7), (8, 9)}):
- This relation is not reflexive because (9, 9) is missing from R.
- It is not transitive because (7, 8) and (8, 7) are related, but (7, 8) and (8, 7) do not imply (7, 7) is related to (7, 7).
Option C (R = {0}):
- This relation is not reflexive because (7, 7), (8, 8), and (9, 9) are missing from R.
- It is transitive because there are no pairs of related elements to violate transitivity.
Option D (R = {(7, 8), (8, 8), (8, 9)}):
- This relation is not reflexive because (7, 7) and (9, 9) are missing from R.
- It is transitive because every pair of related elements has a corresponding chain of related elements.
Conclusion:
Option A (R = {(7, 7), (8, 8), (9, 9)}) is the only relation that is reflexive but not transitive for the set T = {7, 8, 9}.
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 (a, b) and (b, c) in R, (a, c) is also in R. In other words, if there is a chain of two or more related elements, then the first and last elements must also be related.
Analysis of the given options:
Let's analyze each option to determine which one is reflexive but not transitive for the set T = {7, 8, 9}.
Option A (R = {(7, 7), (8, 8), (9, 9)}):
- This relation is reflexive because every element in T is related to itself.
- It is not transitive because there is no chain of related elements. For example, (7, 7) and (7, 7) are related, but (7, 7) and (7, 7) do not imply (7, 7) is related to (7, 7).
Option B (R = {(7, 8), (8, 7), (8, 9)}):
- This relation is not reflexive because (9, 9) is missing from R.
- It is not transitive because (7, 8) and (8, 7) are related, but (7, 8) and (8, 7) do not imply (7, 7) is related to (7, 7).
Option C (R = {0}):
- This relation is not reflexive because (7, 7), (8, 8), and (9, 9) are missing from R.
- It is transitive because there are no pairs of related elements to violate transitivity.
Option D (R = {(7, 8), (8, 8), (8, 9)}):
- This relation is not reflexive because (7, 7) and (9, 9) are missing from R.
- It is transitive because every pair of related elements has a corresponding chain of related elements.
Conclusion:
Option A (R = {(7, 7), (8, 8), (9, 9)}) is the only relation that is reflexive but not transitive for the set T = {7, 8, 9}.
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Community Answer
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 the set T = {7, 8, 9}?a)R = {(7, 7), (8, 8), (9, 9)}b)R = {(7, 8), (8, 7), (8, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'A'. 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, 7), (8, 8), (9, 9)}b)R = {(7, 8), (8, 7), (8, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'A'. 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, 7), (8, 8), (9, 9)}b)R = {(7, 8), (8, 7), (8, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'A'. 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, 7), (8, 8), (9, 9)}b)R = {(7, 8), (8, 7), (8, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'A'. 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, 7), (8, 8), (9, 9)}b)R = {(7, 8), (8, 7), (8, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'A'. 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, 7), (8, 8), (9, 9)}b)R = {(7, 8), (8, 7), (8, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'A'. 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, 7), (8, 8), (9, 9)}b)R = {(7, 8), (8, 7), (8, 9)}c)R = {0}d)R = {(7, 8), (8, 8), (8, 9)}Correct answer is option 'A'. Can you explain this answer?.
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