GATE Exam > GATE Questions > Consider the following statements:S1: The nu...
Start Learning for Free
Consider the following statements:
S1: The number of relations which are both reflexive and asymmetric is 0
S2: The number of relations which are both symmetric and asymmetric is 0
Which option is correct :
- a)Only S1 is true
- b)Only S2 is true
- c)Both are true
- d)None is true
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider the following statements:S1: The number of relations which a...
S1: No relation is possible which is both reflexive and asymmetric because to be reflexive, all self-loops must be there but asymmetric doesn’t allow self-loops. Hence 0 relations.
S2: Only a single relation, i.e. empty relation is both symmetric and asymmetric.
So only S1 is correct.
Most Upvoted Answer
Consider the following statements:S1: The number of relations which a...
The given statements are:
S1: The number of relations which are both reflexive and asymmetric is 0.
S2: The number of relations which are both symmetric and asymmetric is 0.
Explanation:
To understand the given statements, let's first define what reflexive, symmetric, and asymmetric relations are:
- A relation R on a set A is said to be reflexive if every element of A is related to itself. In other words, (a, a) ∈ R for every a ∈ A.
- A relation R on a set A is said to be symmetric if for every pair (a, b) ∈ R, the pair (b, a) is also in R.
- A relation R on a set A is said to be asymmetric if for every pair (a, b) ∈ R, the pair (b, a) is not in R.
S1: The number of relations which are both reflexive and asymmetric is 0.
For a relation to be both reflexive and asymmetric, it should satisfy the following conditions:
- For every element a in the set A, (a, a) should be in the relation R (reflexive property).
- For every pair (a, b) in the relation R, (b, a) should not be in the relation R (asymmetric property).
However, these conditions cannot be simultaneously satisfied because if (a, a) is in the relation R (reflexive property), then (a, a) = (a, a) (symmetric property). Hence, S1 is true.
S2: The number of relations which are both symmetric and asymmetric is 0.
For a relation to be both symmetric and asymmetric, it should satisfy the following conditions:
- For every pair (a, b) in the relation R, (b, a) should also be in the relation R (symmetric property).
- For every pair (a, b) in the relation R, (b, a) should not be in the relation R (asymmetric property).
These conditions cannot be simultaneously satisfied because if (a, b) is in the relation R (symmetric property), then (b, a) = (a, b) (symmetric property). Hence, S2 is true.
Conclusion:
Based on the explanations above, it can be concluded that only statement S1 is true. The number of relations that are both reflexive and asymmetric is indeed 0.
S1: The number of relations which are both reflexive and asymmetric is 0.
S2: The number of relations which are both symmetric and asymmetric is 0.
Explanation:
To understand the given statements, let's first define what reflexive, symmetric, and asymmetric relations are:
- A relation R on a set A is said to be reflexive if every element of A is related to itself. In other words, (a, a) ∈ R for every a ∈ A.
- A relation R on a set A is said to be symmetric if for every pair (a, b) ∈ R, the pair (b, a) is also in R.
- A relation R on a set A is said to be asymmetric if for every pair (a, b) ∈ R, the pair (b, a) is not in R.
S1: The number of relations which are both reflexive and asymmetric is 0.
For a relation to be both reflexive and asymmetric, it should satisfy the following conditions:
- For every element a in the set A, (a, a) should be in the relation R (reflexive property).
- For every pair (a, b) in the relation R, (b, a) should not be in the relation R (asymmetric property).
However, these conditions cannot be simultaneously satisfied because if (a, a) is in the relation R (reflexive property), then (a, a) = (a, a) (symmetric property). Hence, S1 is true.
S2: The number of relations which are both symmetric and asymmetric is 0.
For a relation to be both symmetric and asymmetric, it should satisfy the following conditions:
- For every pair (a, b) in the relation R, (b, a) should also be in the relation R (symmetric property).
- For every pair (a, b) in the relation R, (b, a) should not be in the relation R (asymmetric property).
These conditions cannot be simultaneously satisfied because if (a, b) is in the relation R (symmetric property), then (b, a) = (a, b) (symmetric property). Hence, S2 is true.
Conclusion:
Based on the explanations above, it can be concluded that only statement S1 is true. The number of relations that are both reflexive and asymmetric is indeed 0.
|
Explore Courses for GATE exam
|
|
Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer?
Question Description
Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer?.
Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following statements:S1: The number of relations which are both reflexive and asymmetric is 0S2: The number of relations which are both symmetric and asymmetric is 0Which option is correct :a)Only S1 is trueb)Only S2 is truec)Both are trued)None is trueCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE 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
|
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