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Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R is
- a)R is reflexive and symmetric but not transitive.
- b)R is symmetric and transitive but not reflexive.
- c)R is an equivalence relation.
- d)R is reflexive and transitive but not symmetric.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2...
R be the relation in the set {1,2,3,4] given by R ={(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)}
it is seen that (a,a)∈ R for every a∈{1,2,3,4}
so,R is feflexive.
it is seen that (a,b) = (b,a) ∈ R
because, (1,2)∈ R but (2,1) ∉R
so, R is not symmetric.
it is seen that (a, b), (b, c) ∈ R ⇒ (a, c) ∈ R for all a, b, c ∈ {1, 2, 3, 4}.
so, R is transitive.
Hence, R is reflexive and transitive but not symmetric.
Most Upvoted Answer
Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2...
The relation R on the set {1, 2, 3, 4} is given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}.
Let's analyze the properties of the relation R to determine its characteristics.
1. Reflexivity:
A relation is reflexive if every element in the set is related to itself. In other words, for every element a in the set, (a, a) must be in the relation.
In this case, we have (1, 1), (2, 2), (3, 3), and (4, 4) in the relation R. Therefore, R is reflexive.
2. Symmetry:
A relation is symmetric if whenever (a, b) is in the relation, then (b, a) is also in the relation.
In this case, we have (1, 2) in the relation R, but (2, 1) is not in the relation. Therefore, R is not symmetric.
3. Transitivity:
A relation is transitive if whenever (a, b) and (b, c) are in the relation, then (a, c) is also in the relation.
In this case, we have (1, 2) and (2, 2) in the relation R, but (1, 2) is not related to (2, 2). Therefore, R is not transitive.
Based on the analysis of the properties, we can conclude that R is reflexive and transitive, but not symmetric. Hence, the correct answer is option 'D' - R is reflexive and transitive but not symmetric.
Let's analyze the properties of the relation R to determine its characteristics.
1. Reflexivity:
A relation is reflexive if every element in the set is related to itself. In other words, for every element a in the set, (a, a) must be in the relation.
In this case, we have (1, 1), (2, 2), (3, 3), and (4, 4) in the relation R. Therefore, R is reflexive.
2. Symmetry:
A relation is symmetric if whenever (a, b) is in the relation, then (b, a) is also in the relation.
In this case, we have (1, 2) in the relation R, but (2, 1) is not in the relation. Therefore, R is not symmetric.
3. Transitivity:
A relation is transitive if whenever (a, b) and (b, c) are in the relation, then (a, c) is also in the relation.
In this case, we have (1, 2) and (2, 2) in the relation R, but (1, 2) is not related to (2, 2). Therefore, R is not transitive.
Based on the analysis of the properties, we can conclude that R is reflexive and transitive, but not symmetric. Hence, the correct answer is option 'D' - R is reflexive and transitive but not symmetric.
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Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2...
Option D is correct...
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Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer?
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Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer?.
Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R isa)R is reflexive and symmetric but not transitive.b)R is symmetric and transitive but not reflexive.c)R is an equivalence relation.d)R is reflexive and transitive but not symmetric.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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