Defence Exam > Defence Questions > Let X be the set of all citizens of India. El...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup