Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > What is the nature of relation R, if R is def...
Start Learning for Free
What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?
- a)reflexive
- b)symmetric
- c)transitive
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
What is the nature of relation R, if R is defined as R = {(x, y) : 2x ...
Let us check all the conditions:
Reflexivity:
Let x be an arbitrary element of R. For Reflexive, let y + x
i.e. for any x ∈ R
⇒ 2x + x = 41
Let x be an arbitrary element of R. For Reflexive, let y + x
i.e. for any x ∈ R
⇒ 2x + x = 41
Thus, it is NOT reflexive.
Symmetry:
Let (x, y) ∈ R. Then,
2x + y = 41 Which is not equal to 2y + x = 41
i.e. (y , x) ∉ R
So, R is NOT symmetric.
Let (x, y) ∈ R. Then,
2x + y = 41 Which is not equal to 2y + x = 41
i.e. (y , x) ∉ R
So, R is NOT symmetric.
Transitivity:
Let (x, y) and (y, z) ∈ R
⇒ 2x + y = 41 and 2y + z = 41
which is not equal to 2x + z = 41
i.e. (x , z) ∉ R
Thus, R is NOT transitive.
Let (x, y) and (y, z) ∈ R
⇒ 2x + y = 41 and 2y + z = 41
which is not equal to 2x + z = 41
i.e. (x , z) ∉ R
Thus, R is NOT transitive.
Free Test
FREE
| Start Free Test |
Community Answer
What is the nature of relation R, if R is defined as R = {(x, y) : 2x ...
Understanding Relation R
The relation R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}. To analyze the properties of this relation, we will evaluate its reflexivity, symmetry, and transitivity.
Reflexivity
- A relation R is reflexive if for every element a in the set, (a, a) ∈ R.
- In this case, for any natural number x, we need to check if (x, x) satisfies the equation 2x + x = 41.
- This simplifies to 3x = 41, which has no natural number solution.
- Therefore, R is not reflexive.
Symmetry
- A relation R is symmetric if for every (a, b) ∈ R, (b, a) ∈ R also holds true.
- If we take (x, y) such that 2x + y = 41, then to check symmetry, we would need 2y + x = 41 for (y, x).
- Rearranging gives us x = 41 - 2y, which does not guarantee that both pairs will exist.
- Thus, R is not symmetric.
Transitivity
- A relation R is transitive if for any (a, b) and (b, c) in R, (a, c) must also be in R.
- Given the structure of R, finding pairs (x, y) and (y, z) that satisfy both equations is complex and does not guarantee that (x, z) will also satisfy the equation.
- Therefore, R is not transitive.
Conclusion
Since R does not satisfy any of the properties of reflexivity, symmetry, or transitivity, the correct answer is option 'D' - None of these.
The relation R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}. To analyze the properties of this relation, we will evaluate its reflexivity, symmetry, and transitivity.
Reflexivity
- A relation R is reflexive if for every element a in the set, (a, a) ∈ R.
- In this case, for any natural number x, we need to check if (x, x) satisfies the equation 2x + x = 41.
- This simplifies to 3x = 41, which has no natural number solution.
- Therefore, R is not reflexive.
Symmetry
- A relation R is symmetric if for every (a, b) ∈ R, (b, a) ∈ R also holds true.
- If we take (x, y) such that 2x + y = 41, then to check symmetry, we would need 2y + x = 41 for (y, x).
- Rearranging gives us x = 41 - 2y, which does not guarantee that both pairs will exist.
- Thus, R is not symmetric.
Transitivity
- A relation R is transitive if for any (a, b) and (b, c) in R, (a, c) must also be in R.
- Given the structure of R, finding pairs (x, y) and (y, z) that satisfy both equations is complex and does not guarantee that (x, z) will also satisfy the equation.
- Therefore, R is not transitive.
Conclusion
Since R does not satisfy any of the properties of reflexivity, symmetry, or transitivity, the correct answer is option 'D' - None of these.
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer?.
What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y ∈ N}?a)reflexiveb)symmetricc)transitived)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup