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Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?
- a)The relation is an equivalence relation on X.
- b)The relation is symmetric but neither reflexive nor transitive.
- c)The relation is reflexive but neither, symmetric nor transitive.
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let X be the set of all citizens of India. Elements x, y in X aresaid ...
X = Set of all citizens of India
(R is not reflexive)
(R is symmetric)
(R is not transitive)
(R is not reflexive) (R is symmetric)(R is not transitive)Most Upvoted Answer
Let X be the set of all citizens of India. Elements x, y in X aresaid ...
Explanation:
Relation on a set is a way of comparing its elements based on some property. In this case, we are comparing citizens of India based on the difference in their ages.
Reflexive: A relation is reflexive if every element is related to itself.
- In this case, x and x have a difference of 0 years, which is not 5 years. Hence, the relation is not reflexive.
Symmetric: A relation is symmetric if whenever x is related to y, y is also related to x.
- If x is related to y, then the difference in their ages is 5 years.
- If y is related to x, then the difference in their ages is -5 years (since we are only considering positive differences).
- Therefore, the relation is not symmetric.
Transitive: A relation is transitive if whenever x is related to y and y is related to z, then x is related to z.
- If x is related to y, then the difference in their ages is 5 years.
- If y is related to z, then the difference in their ages is 5 years.
- Therefore, x is related to z, and the relation is transitive.
Conclusion:
Since the relation is not reflexive or symmetric but is transitive, the only correct option is B.
Relation on a set is a way of comparing its elements based on some property. In this case, we are comparing citizens of India based on the difference in their ages.
Reflexive: A relation is reflexive if every element is related to itself.
- In this case, x and x have a difference of 0 years, which is not 5 years. Hence, the relation is not reflexive.
Symmetric: A relation is symmetric if whenever x is related to y, y is also related to x.
- If x is related to y, then the difference in their ages is 5 years.
- If y is related to x, then the difference in their ages is -5 years (since we are only considering positive differences).
- Therefore, the relation is not symmetric.
Transitive: A relation is transitive if whenever x is related to y and y is related to z, then x is related to z.
- If x is related to y, then the difference in their ages is 5 years.
- If y is related to z, then the difference in their ages is 5 years.
- Therefore, x is related to z, and the relation is transitive.
Conclusion:
Since the relation is not reflexive or symmetric but is transitive, the only correct option is B.
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Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?a)The relation is an equivalence relation on X.b)The relation is symmetric but neither reflexive nor transitive.c)The relation is reflexive but neither, symmetric nor transitive.d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?a)The relation is an equivalence relation on X.b)The relation is symmetric but neither reflexive nor transitive.c)The relation is reflexive but neither, symmetric nor transitive.d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?a)The relation is an equivalence relation on X.b)The relation is symmetric but neither reflexive nor transitive.c)The relation is reflexive but neither, symmetric nor transitive.d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?a)The relation is an equivalence relation on X.b)The relation is symmetric but neither reflexive nor transitive.c)The relation is reflexive but neither, symmetric nor transitive.d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?a)The relation is an equivalence relation on X.b)The relation is symmetric but neither reflexive nor transitive.c)The relation is reflexive but neither, symmetric nor transitive.d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?a)The relation is an equivalence relation on X.b)The relation is symmetric but neither reflexive nor transitive.c)The relation is reflexive but neither, symmetric nor transitive.d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?a)The relation is an equivalence relation on X.b)The relation is symmetric but neither reflexive nor transitive.c)The relation is reflexive but neither, symmetric nor transitive.d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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