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Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. Which one of the following statements is correct?
- a)Relation is symmetric and transitive only
- b)Relation is reflexive and transitive only
- c)Relation is reflexive and symmetric only
- d)Relation is reflexive symmetric and transitive
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let X be the set of all graduates in India. Elements x and y in X are ...
xRy ⇒ x and y are graduates of the same university.
Reflexive xRx ⇔ x and y are graduates of the same university.
So, relation is reflexive.
Symmetric xRy ⇔ x and y are graduates of the same university.
implies, yRx ⇔ y and x are graduates of the same university.
So, relation is symmetric.
Transitive xRy, yRz ⇔ xRz
It means x and y, y and z are graduates of the same university, then x and z are also graduates of the same university.
So, relation is transitive.
Hence, relation is reflexive, symmetric and transitive.
Reflexive xRx ⇔ x and y are graduates of the same university.
So, relation is reflexive.
Symmetric xRy ⇔ x and y are graduates of the same university.
implies, yRx ⇔ y and x are graduates of the same university.
So, relation is symmetric.
Transitive xRy, yRz ⇔ xRz
It means x and y, y and z are graduates of the same university, then x and z are also graduates of the same university.
So, relation is transitive.
Hence, relation is reflexive, symmetric and transitive.
Most Upvoted Answer
Let X be the set of all graduates in India. Elements x and y in X are ...
Explanation:
The given relation defines a relation on the set of all graduates in India. Let's analyze each property of the relation.
Reflexivity:
A relation is reflexive if every element is related to itself. In this case, every graduate is a graduate of the same university as themselves. Therefore, the relation is reflexive.
Symmetry:
A relation is symmetric if whenever x is related to y, then y is related to x. In this case, if x and y are graduates of the same university, then y and x are also graduates of the same university. Therefore, the relation is symmetric.
Transitivity:
A relation is transitive if whenever x is related to y and y is related to z, then x is related to z. In this case, if x and y are graduates of the same university, and y and z are graduates of the same university, then x and z are also graduates of the same university. Therefore, the relation is transitive.
Since the relation satisfies all three properties (reflexivity, symmetry, and transitivity), it is a reflexive, symmetric, and transitive relation. Therefore, the correct answer is option 'd'.
The given relation defines a relation on the set of all graduates in India. Let's analyze each property of the relation.
Reflexivity:
A relation is reflexive if every element is related to itself. In this case, every graduate is a graduate of the same university as themselves. Therefore, the relation is reflexive.
Symmetry:
A relation is symmetric if whenever x is related to y, then y is related to x. In this case, if x and y are graduates of the same university, then y and x are also graduates of the same university. Therefore, the relation is symmetric.
Transitivity:
A relation is transitive if whenever x is related to y and y is related to z, then x is related to z. In this case, if x and y are graduates of the same university, and y and z are graduates of the same university, then x and z are also graduates of the same university. Therefore, the relation is transitive.
Since the relation satisfies all three properties (reflexivity, symmetry, and transitivity), it is a reflexive, symmetric, and transitive relation. Therefore, the correct answer is option 'd'.
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Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. Which one of the following statements is correct?a)Relation is symmetric and transitive onlyb)Relation is reflexive and transitive onlyc)Relation is reflexive and symmetric onlyd)Relation is reflexive symmetric and transitiveCorrect answer is option 'D'. Can you explain this answer?
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Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. Which one of the following statements is correct?a)Relation is symmetric and transitive onlyb)Relation is reflexive and transitive onlyc)Relation is reflexive and symmetric onlyd)Relation is reflexive symmetric and transitiveCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. Which one of the following statements is correct?a)Relation is symmetric and transitive onlyb)Relation is reflexive and transitive onlyc)Relation is reflexive and symmetric onlyd)Relation is reflexive symmetric and transitiveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. Which one of the following statements is correct?a)Relation is symmetric and transitive onlyb)Relation is reflexive and transitive onlyc)Relation is reflexive and symmetric onlyd)Relation is reflexive symmetric and transitiveCorrect answer is option 'D'. Can you explain this answer?.
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