Class 12 Exam > Class 12 Questions > Which of the following relations is transitiv...
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Which of the following relations is transitive but not reflexive for the set S = {3, 4, 6}?
- a)R = {(3, 4), (4, 6), (3, 6)}
- b)R = {(1, 2), (1, 3), (1, 4)}
- c)R = {(3, 3), (4, 4), (6, 6)}
- d)R = {(3, 4), (4, 3)}
Correct answer is option 'A'. Can you explain this answer?
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Which of the following relations is transitive but not reflexive for t...
Transitive and Reflexive Relations:
A relation on a set is said to be transitive if for every three elements (a, b, c) in the set, if (a, b) and (b, c) are both in the relation, then (a, c) must also be in the relation.
A relation on a set is said to be reflexive if every element in the set is related to itself.
Given:
Set S = {3, 4, 6}
We need to determine which of the given relations is transitive but not reflexive.
Solution:
Let's analyze each option one by one:
Option a) R = {(3, 4), (4, 6), (3, 6)}
- To check transitivity, we need to consider all possible combinations of three elements (a, b, c) from the set.
- Let's consider (3, 4), (4, 6), and (3, 6).
- (3, 4) and (4, 6) are both in the relation.
- Therefore, by transitivity, (3, 6) should also be in the relation.
- (3, 6) is indeed in the relation.
- Hence, this relation is transitive.
- However, this relation is not reflexive because (3, 3), (4, 4), and (6, 6) are not in the relation.
- Therefore, option a) is the correct answer.
Option b) R = {(1, 2), (1, 3), (1, 4)}
- This relation does not contain any elements from the set S = {3, 4, 6}.
- Therefore, this relation is not transitive and not reflexive.
Option c) R = {(3, 3), (4, 4), (6, 6)}
- This relation contains all possible reflexive pairs.
- However, it does not contain any pairs for transitivity.
- Therefore, this relation is reflexive but not transitive.
Option d) R = {(3, 4), (4, 3)}
- This relation contains two pairs (3, 4) and (4, 3).
- It does not contain any pairs for transitivity.
- Therefore, this relation is not transitive and not reflexive.
Conclusion:
Among the given options, option a) R = {(3, 4), (4, 6), (3, 6)} is the only relation that is transitive but not reflexive.
A relation on a set is said to be transitive if for every three elements (a, b, c) in the set, if (a, b) and (b, c) are both in the relation, then (a, c) must also be in the relation.
A relation on a set is said to be reflexive if every element in the set is related to itself.
Given:
Set S = {3, 4, 6}
We need to determine which of the given relations is transitive but not reflexive.
Solution:
Let's analyze each option one by one:
Option a) R = {(3, 4), (4, 6), (3, 6)}
- To check transitivity, we need to consider all possible combinations of three elements (a, b, c) from the set.
- Let's consider (3, 4), (4, 6), and (3, 6).
- (3, 4) and (4, 6) are both in the relation.
- Therefore, by transitivity, (3, 6) should also be in the relation.
- (3, 6) is indeed in the relation.
- Hence, this relation is transitive.
- However, this relation is not reflexive because (3, 3), (4, 4), and (6, 6) are not in the relation.
- Therefore, option a) is the correct answer.
Option b) R = {(1, 2), (1, 3), (1, 4)}
- This relation does not contain any elements from the set S = {3, 4, 6}.
- Therefore, this relation is not transitive and not reflexive.
Option c) R = {(3, 3), (4, 4), (6, 6)}
- This relation contains all possible reflexive pairs.
- However, it does not contain any pairs for transitivity.
- Therefore, this relation is reflexive but not transitive.
Option d) R = {(3, 4), (4, 3)}
- This relation contains two pairs (3, 4) and (4, 3).
- It does not contain any pairs for transitivity.
- Therefore, this relation is not transitive and not reflexive.
Conclusion:
Among the given options, option a) R = {(3, 4), (4, 6), (3, 6)} is the only relation that is transitive but not reflexive.
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Community Answer
Which of the following relations is transitive but not reflexive for t...
For the above given set S = {3, 4, 6}, R = {(3, 4), (4, 6), (3, 6)} is transitive as (3,4)∈R and (4,6) ∈R and (3,6) also belongs to R . It is not a reflexive relation as it does not satisfy the condition (a,a)∈R, for every a∈A for a relation R in the set A.
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Which of the following relations is transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}Correct answer is option 'A'. Can you explain this answer?
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Which of the following relations is transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}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 transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}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 transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}Correct answer is option 'A'. Can you explain this answer?.
Which of the following relations is transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}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 transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}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 transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}Correct answer is option 'A'. Can you explain this answer?.
Solutions for Which of the following relations is transitive but not reflexive for the set S = {3, 4, 6}?a)R = {(3, 4), (4, 6), (3, 6)}b)R = {(1, 2), (1, 3), (1, 4)}c)R = {(3, 3), (4, 4), (6, 6)}d)R = {(3, 4), (4, 3)}Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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