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Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.
- a)R = {(1, 2), (1, 3), (1, 4)}
- b)R = {(1, 2), (2, 1)}
- c)R = {(1, 1), (2, 2), (3, 3)}
- d)R = {(1, 1), (1, 2), (2, 3)}
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Which of the following relations is symmetric but neither reflexive no...
Explanation:
Symmetric Relation:
A relation R on a set A is said to be symmetric if for every (a, b) in R, we also have (b, a) in R. In other words, if (a, b) belongs to R, then (b, a) must also belong to R.
Reflexive Relation:
A relation R on a set A is said to be reflexive if for every element a in A, (a, a) belongs to R. In other words, every element in A is related to itself.
Transitive Relation:
A relation R on a set A is said to be transitive if for every (a, b) and (b, c) in R, we also have (a, c) in R. In other words, if (a, b) and (b, c) belong to R, then (a, c) must also belong to R.
Analysis:
- Option 'a' is not symmetric as it contains (1, 4) without (4, 1).
- Option 'b' is symmetric as it contains (1, 2) and (2, 1), but it is not reflexive as it does not contain (1, 1) and not transitive as it does not contain (1, 1) and (1, 2) implies (1, 2) should be present.
- Option 'c' is reflexive but not symmetric as it contains (1, 1) but not (1, 2).
- Option 'd' is reflexive and transitive but not symmetric as it contains (1, 2) without (2, 1).
Therefore, option 'b' is the correct answer as it is symmetric but neither reflexive nor transitive for the set A = {1, 2, 3}.
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Community Answer
Which of the following relations is symmetric but neither reflexive no...
A relation in a set A is said to be symmetric if (a1, a2)∈R implies that (a1, a2)∈R,for every a1, a2∈R.
Hence, for the given set A={1, 2, 3}, R={(1, 2), (2, 1)} is symmetric. It is not reflexive since every element is not related to itself and neither transitive as it does not satisfy the condition that for a given 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.
Hence, for the given set A={1, 2, 3}, R={(1, 2), (2, 1)} is symmetric. It is not reflexive since every element is not related to itself and neither transitive as it does not satisfy the condition that for a given 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 symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}Correct answer is option 'B'. Can you explain this answer?
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Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}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 symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}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 symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}Correct answer is option 'B'. Can you explain this answer?.
Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}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 symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}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 symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}Correct answer is option 'B'. Can you explain this answer?.
Solutions for Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.a)R = {(1, 2), (1, 3), (1, 4)}b)R = {(1, 2), (2, 1)}c)R = {(1, 1), (2, 2), (3, 3)}d)R = {(1, 1), (1, 2), (2, 3)}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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