Class 12 Exam > Class 12 Questions > Which of the following relations is symmetric...
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Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?
- a)R = {(4, 4), (5, 4), (5, 5)}
- b)R = {(4, 4), (5, 5)}
- c)R = {(4, 5), (5, 4)}
- d)R = {(4, 5), (5, 4), (4, 4)}
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Which of the following relations is symmetric and transitive but not r...
R= {(4, 5), (5, 4), (4, 4)} is symmetric since (4, 5) and (5, 4) are converse of each other thus satisfying the condition for a symmetric relation and it is transitive as (4, 5)∈R and (5, 4)∈R implies that (4, 4) ∈R. It is not reflexive as every element in the set I is not related to itself.
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Which of the following relations is symmetric and transitive but not r...
Symmetric Relation:
A relation R is symmetric if for every (a, b) in R, (b, a) is also in R.
Transitive Relation:
A relation R is transitive if for every (a, b) and (b, c) in R, (a, c) is also in R.
Reflexive Relation:
A relation R is reflexive if for every element a in the set I, (a, a) is in R.
Given:
Set I = {4, 5}
Option A:
R = {(4, 4), (5, 4), (5, 5)}
- (4, 4) is present, but (4, 4) is not present.
- (5, 4) is present, but (4, 5) is not present.
- (5, 5) is present, but (5, 5) is not present.
Option A is not symmetric because (4, 4) does not have a corresponding (4, 4) element.
Option B:
R = {(4, 4), (5, 5)}
- (4, 4) is present, and (4, 4) is present.
- (5, 5) is present, and (5, 5) is present.
Option B is reflexive because (4, 4) and (5, 5) have corresponding elements.
Option C:
R = {(4, 5), (5, 4)}
- (4, 5) is present, but (5, 4) is not present.
- (5, 4) is present, but (4, 5) is not present.
Option C is not transitive because (4, 5) and (5, 4) do not have a corresponding (4, 4) element.
Option D:
R = {(4, 5), (5, 4), (4, 4)}
- (4, 5) is present, and (5, 4) is present.
- (5, 4) is present, and (4, 5) is present.
- (4, 4) is present, and (4, 4) is present.
Option D is symmetric because for every (a, b) in R, (b, a) is also in R.
Option D is transitive because for every (a, b) and (b, c) in R, (a, c) is also in R.
Option D is not reflexive because (5, 5) is not present.
Conclusion:
Among the given options, option D is the only relation that is symmetric and transitive but not reflexive for the set I = {4, 5}.
A relation R is symmetric if for every (a, b) in R, (b, a) is also in R.
Transitive Relation:
A relation R is transitive if for every (a, b) and (b, c) in R, (a, c) is also in R.
Reflexive Relation:
A relation R is reflexive if for every element a in the set I, (a, a) is in R.
Given:
Set I = {4, 5}
Option A:
R = {(4, 4), (5, 4), (5, 5)}
- (4, 4) is present, but (4, 4) is not present.
- (5, 4) is present, but (4, 5) is not present.
- (5, 5) is present, but (5, 5) is not present.
Option A is not symmetric because (4, 4) does not have a corresponding (4, 4) element.
Option B:
R = {(4, 4), (5, 5)}
- (4, 4) is present, and (4, 4) is present.
- (5, 5) is present, and (5, 5) is present.
Option B is reflexive because (4, 4) and (5, 5) have corresponding elements.
Option C:
R = {(4, 5), (5, 4)}
- (4, 5) is present, but (5, 4) is not present.
- (5, 4) is present, but (4, 5) is not present.
Option C is not transitive because (4, 5) and (5, 4) do not have a corresponding (4, 4) element.
Option D:
R = {(4, 5), (5, 4), (4, 4)}
- (4, 5) is present, and (5, 4) is present.
- (5, 4) is present, and (4, 5) is present.
- (4, 4) is present, and (4, 4) is present.
Option D is symmetric because for every (a, b) in R, (b, a) is also in R.
Option D is transitive because for every (a, b) and (b, c) in R, (a, c) is also in R.
Option D is not reflexive because (5, 5) is not present.
Conclusion:
Among the given options, option D is the only relation that is symmetric and transitive but not reflexive for the set I = {4, 5}.
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Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. Can you explain this answer?
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Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. 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 and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. 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 and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. Can you explain this answer?.
Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. 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 and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. 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 and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 4), (5, 5)}c)R = {(4, 5), (5, 4)}d)R = {(4, 5), (5, 4), (4, 4)}Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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