JEE Exam > JEE Questions > Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6...
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Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation is
- a)an equivalence relation
- b)reflexive and symmetric
- c)reflexive and transitive
- d)only reflexive
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (...
Understanding the Relation R
The relation R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} is defined on the set A = {3, 6, 9, 12}. To determine the properties of this relation, we will analyze it for reflexivity, symmetry, and transitivity.
Reflexivity
- A relation is reflexive if every element in A relates to itself.
- For the set A, we check:
- (3, 3), (6, 6), (9, 9), and (12, 12) are present in R.
- Since all elements relate to themselves, R is reflexive.
Symmetry
- A relation is symmetric if for every (a, b) in R, (b, a) must also be in R.
- Checking pairs:
- (6, 12) is in R, but (12, 6) is not.
- Thus, R is not symmetric.
Transitivity
- A relation is transitive if whenever (a, b) and (b, c) are in R, then (a, c) must also be in R.
- Checking pairs:
- From (6, 12) and (3, 6), we can infer (3, 12) which is present in R.
- However, (3, 9) and (9, 12) do not imply (3, 12) being in R, but other pairs can demonstrate transitivity.
- After checking possible combinations, R holds transitive properties.
Conclusion
- R is reflexive and transitive but not symmetric.
- Therefore, the correct classification of relation R is that it is reflexive and transitive.
Thus, the answer is indeed option 'C'.
The relation R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} is defined on the set A = {3, 6, 9, 12}. To determine the properties of this relation, we will analyze it for reflexivity, symmetry, and transitivity.
Reflexivity
- A relation is reflexive if every element in A relates to itself.
- For the set A, we check:
- (3, 3), (6, 6), (9, 9), and (12, 12) are present in R.
- Since all elements relate to themselves, R is reflexive.
Symmetry
- A relation is symmetric if for every (a, b) in R, (b, a) must also be in R.
- Checking pairs:
- (6, 12) is in R, but (12, 6) is not.
- Thus, R is not symmetric.
Transitivity
- A relation is transitive if whenever (a, b) and (b, c) are in R, then (a, c) must also be in R.
- Checking pairs:
- From (6, 12) and (3, 6), we can infer (3, 12) which is present in R.
- However, (3, 9) and (9, 12) do not imply (3, 12) being in R, but other pairs can demonstrate transitivity.
- After checking possible combinations, R holds transitive properties.
Conclusion
- R is reflexive and transitive but not symmetric.
- Therefore, the correct classification of relation R is that it is reflexive and transitive.
Thus, the answer is indeed option 'C'.
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Community Answer
Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (...
(3, 3), (6, 6), (9, 9), (12, 12), ∈R. R is not symmetric as (6, 12) ∈R but (12, 6) ÎR.
R is transitive as the only pair which
needs verification is (3, 6) and (6, 12) ∈R.
R is transitive as the only pair which
needs verification is (3, 6) and (6, 12) ∈R.
⇒ (3, 12) ∈ R
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Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. Can you explain this answer?
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Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. 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 = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. 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 = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. Can you explain this answer?.
Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. 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 = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. 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 = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. Can you explain this answer?.
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Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, the relation isa)an equivalence relationb)reflexive and symmetricc)reflexive and transitived)only reflexiveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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