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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, 5), (5, 4), (4, 4)}
- c)R = {(4, 4), (5, 5)}
- d)R = {(4, 5), (5, 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...
Symmetric Relation:
A relation R is said to be symmetric if for every (a, b) ∈ R, (b, a) ∈ R.
In other words, if (a, b) is in the relation, then (b, a) should also be in the relation.
Transitive Relation:
A relation R is said to be transitive if for every (a, b) ∈ R and (b, c) ∈ R, (a, c) ∈ R.
In other words, if (a, b) and (b, c) are in the relation, then (a, c) should also be in the relation.
Reflexive Relation:
A relation R is said to be reflexive if for every element a in the set I, (a, a) ∈ R.
In other words, every element of the set should be related to itself.
Given Relations:
a) R = {(4, 4), (5, 4), (5, 5)}
b) R = {(4, 5), (5, 4), (4, 4)}
c) R = {(4, 4), (5, 5)}
d) R = {(4, 5), (5, 4)}
Analysis:
We need to find a relation that is symmetric and transitive but not reflexive for the set I = {4, 5}.
Option a: R = {(4, 4), (5, 4), (5, 5)}
- (4, 4) is reflexive.
- (5, 4) is not symmetric because (4, 5) is not in the relation.
- (5, 5) is reflexive.
- Not transitive because (4, 4) and (4, 5) are in the relation, but (5, 5) is not in the relation.
Option b: R = {(4, 5), (5, 4), (4, 4)}
- (4, 5) is not reflexive.
- (5, 4) is not symmetric because (4, 5) is not in the relation.
- (4, 4) is reflexive.
- Not transitive because (4, 5) and (5, 4) are in the relation, but (4, 4) is not in the relation.
Option c: R = {(4, 4), (5, 5)}
- (4, 4) is reflexive.
- (5, 5) is reflexive.
- Not symmetric because (4, 4) and (5, 5) are in the relation, but (5, 4) is not in the relation.
- Not transitive because (4, 4) and (5, 5) are in the relation, but (4, 5) is not in the relation.
Option d: R = {(4, 5), (5, 4)}
- (4, 5) is not reflexive.
- (5, 4) is not reflexive.
- Symmetric because (4, 5) and (5,
A relation R is said to be symmetric if for every (a, b) ∈ R, (b, a) ∈ R.
In other words, if (a, b) is in the relation, then (b, a) should also be in the relation.
Transitive Relation:
A relation R is said to be transitive if for every (a, b) ∈ R and (b, c) ∈ R, (a, c) ∈ R.
In other words, if (a, b) and (b, c) are in the relation, then (a, c) should also be in the relation.
Reflexive Relation:
A relation R is said to be reflexive if for every element a in the set I, (a, a) ∈ R.
In other words, every element of the set should be related to itself.
Given Relations:
a) R = {(4, 4), (5, 4), (5, 5)}
b) R = {(4, 5), (5, 4), (4, 4)}
c) R = {(4, 4), (5, 5)}
d) R = {(4, 5), (5, 4)}
Analysis:
We need to find a relation that is symmetric and transitive but not reflexive for the set I = {4, 5}.
Option a: R = {(4, 4), (5, 4), (5, 5)}
- (4, 4) is reflexive.
- (5, 4) is not symmetric because (4, 5) is not in the relation.
- (5, 5) is reflexive.
- Not transitive because (4, 4) and (4, 5) are in the relation, but (5, 5) is not in the relation.
Option b: R = {(4, 5), (5, 4), (4, 4)}
- (4, 5) is not reflexive.
- (5, 4) is not symmetric because (4, 5) is not in the relation.
- (4, 4) is reflexive.
- Not transitive because (4, 5) and (5, 4) are in the relation, but (4, 4) is not in the relation.
Option c: R = {(4, 4), (5, 5)}
- (4, 4) is reflexive.
- (5, 5) is reflexive.
- Not symmetric because (4, 4) and (5, 5) are in the relation, but (5, 4) is not in the relation.
- Not transitive because (4, 4) and (5, 5) are in the relation, but (4, 5) is not in the relation.
Option d: R = {(4, 5), (5, 4)}
- (4, 5) is not reflexive.
- (5, 4) is not reflexive.
- Symmetric because (4, 5) and (5,
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Community 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 reflexive for the set I = {4, 5}?a)R = {(4, 4), (5, 4), (5, 5)}b)R = {(4, 5), (5, 4), (4, 4)}c)R = {(4, 4), (5, 5)}d)R = {(4, 5), (5, 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, 5), (5, 4), (4, 4)}c)R = {(4, 4), (5, 5)}d)R = {(4, 5), (5, 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, 5), (5, 4), (4, 4)}c)R = {(4, 4), (5, 5)}d)R = {(4, 5), (5, 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, 5), (5, 4), (4, 4)}c)R = {(4, 4), (5, 5)}d)R = {(4, 5), (5, 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, 5), (5, 4), (4, 4)}c)R = {(4, 4), (5, 5)}d)R = {(4, 5), (5, 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, 5), (5, 4), (4, 4)}c)R = {(4, 4), (5, 5)}d)R = {(4, 5), (5, 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, 5), (5, 4), (4, 4)}c)R = {(4, 4), (5, 5)}d)R = {(4, 5), (5, 4)}Correct answer is option 'D'. Can you explain this answer?.
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