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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...
Transitivity and Reflexivity
To determine if a relation is transitive, we need to check if whenever there are two pairs (a, b) and (b, c) in the relation, then the pair (a, c) is also in the relation. In other words, if (a, b) and (b, c) are in the relation, then (a, c) should also be in the relation.
On the other hand, reflexivity means that every element in the set is related to itself. In other words, for every element a in the set, (a, a) should be in the relation.
Given Set and Relations
The given set S = {3, 4, 6} consists of three elements.
Let's analyze each relation to determine if it is transitive and reflexive:
Option a) R = {(3, 4), (4, 6), (3, 6)}
- This relation is transitive because if we have (3, 4) and (4, 6), it implies that (3, 6) should also be in the relation.
- However, this relation is not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
Option b) R = {(1, 2), (1, 3), (1, 4)}
- This relation is not transitive because there are no pairs (a, c) such that (a, b) and (b, c) are both in the relation.
- This relation is also not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
Option c) R = {(3, 3), (4, 4), (6, 6)}
- This relation is reflexive because it contains the pairs (3, 3), (4, 4), and (6, 6).
- However, this relation is not transitive because there are no pairs (a, c) such that (a, b) and (b, c) are both in the relation.
Option d) R = {(3, 4), (4, 3)}
- This relation is not transitive because it does not contain the pair (3, 3) or (4, 4) to satisfy the transitive property.
- This relation is not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
Conclusion
Among the given options, only option a) R = {(3, 4), (4, 6), (3, 6)} is transitive because it satisfies the condition that if (a, b) and (b, c) are in the relation, then (a, c) should also be in the relation. However, it is not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
To determine if a relation is transitive, we need to check if whenever there are two pairs (a, b) and (b, c) in the relation, then the pair (a, c) is also in the relation. In other words, if (a, b) and (b, c) are in the relation, then (a, c) should also be in the relation.
On the other hand, reflexivity means that every element in the set is related to itself. In other words, for every element a in the set, (a, a) should be in the relation.
Given Set and Relations
The given set S = {3, 4, 6} consists of three elements.
Let's analyze each relation to determine if it is transitive and reflexive:
Option a) R = {(3, 4), (4, 6), (3, 6)}
- This relation is transitive because if we have (3, 4) and (4, 6), it implies that (3, 6) should also be in the relation.
- However, this relation is not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
Option b) R = {(1, 2), (1, 3), (1, 4)}
- This relation is not transitive because there are no pairs (a, c) such that (a, b) and (b, c) are both in the relation.
- This relation is also not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
Option c) R = {(3, 3), (4, 4), (6, 6)}
- This relation is reflexive because it contains the pairs (3, 3), (4, 4), and (6, 6).
- However, this relation is not transitive because there are no pairs (a, c) such that (a, b) and (b, c) are both in the relation.
Option d) R = {(3, 4), (4, 3)}
- This relation is not transitive because it does not contain the pair (3, 3) or (4, 4) to satisfy the transitive property.
- This relation is not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
Conclusion
Among the given options, only option a) R = {(3, 4), (4, 6), (3, 6)} is transitive because it satisfies the condition that if (a, b) and (b, c) are in the relation, then (a, c) should also be in the relation. However, it is not reflexive because it does not contain the pairs (3, 3), (4, 4), and (6, 6).
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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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