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If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?
- a)R is reflexive and symmetric, but not transitive
- b)R is reflexive and transitive, but not symmetric
- c)R is reflexive, but neither symmetric nor transitive
- d)R is reflexive, symmetric and transitive
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, ...
Since, (a, a), (b, b), (c, c) ε R
Therefore, R is a reflexive relation
But, (a,b ) ε R and (b, a) R So, R is not a symmetric relation Also, (a, b), (b, cj 6 R.
Implies (a, c)
Hence, R is not a transitive relation
Therefore, R is a reflexive relation
But, (a,b ) ε R and (b, a) R So, R is not a symmetric relation Also, (a, b), (b, cj 6 R.
Implies (a, c)
Hence, R is not a transitive relation
Most Upvoted Answer
If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, ...
Since, (a, a), (b, b), (c, c) ε R
Therefore, R is a reflexive relation
But, (a,b ) ε R and (b, a) R So, R is not a symmetric relation Also, (a, b), (b, cj 6 R.
Implies (a, c)
Hence, R is not a transitive relation
Therefore, R is a reflexive relation
But, (a,b ) ε R and (b, a) R So, R is not a symmetric relation Also, (a, b), (b, cj 6 R.
Implies (a, c)
Hence, R is not a transitive relation
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Community Answer
If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, ...
Given:
A = {a, b, c}
R = {(a, a), (a, b), (b, c), (b, b), (c, c), (c, a)}
To determine:
The properties of the binary relation R.
Solution:
Reflexivity:
A binary relation R on a set A is reflexive if every element in A is related to itself. In other words, for every element a in A, (a, a) must be in R.
In the given relation R, we can see that (a, a), (b, b), and (c, c) are present. Therefore, R is reflexive.
Symmetry:
A binary relation R on a set A is symmetric if for every pair (a, b) in R, the pair (b, a) is also in R.
In the given relation R, we can see that (a, b) is present, but (b, a) is not present. Therefore, R is not symmetric.
Transitivity:
A binary relation R on a set A is transitive if for every three elements a, b, and c in A, if (a, b) and (b, c) are in R, then (a, c) must also be in R.
In the given relation R, we can see that (a, b) and (b, c) are present, but (a, c) is not present. Therefore, R is not transitive.
Conclusion:
From the above analysis, we can conclude that R is reflexive, but neither symmetric nor transitive. Therefore, the correct answer is option C.
A = {a, b, c}
R = {(a, a), (a, b), (b, c), (b, b), (c, c), (c, a)}
To determine:
The properties of the binary relation R.
Solution:
Reflexivity:
A binary relation R on a set A is reflexive if every element in A is related to itself. In other words, for every element a in A, (a, a) must be in R.
In the given relation R, we can see that (a, a), (b, b), and (c, c) are present. Therefore, R is reflexive.
Symmetry:
A binary relation R on a set A is symmetric if for every pair (a, b) in R, the pair (b, a) is also in R.
In the given relation R, we can see that (a, b) is present, but (b, a) is not present. Therefore, R is not symmetric.
Transitivity:
A binary relation R on a set A is transitive if for every three elements a, b, and c in A, if (a, b) and (b, c) are in R, then (a, c) must also be in R.
In the given relation R, we can see that (a, b) and (b, c) are present, but (a, c) is not present. Therefore, R is not transitive.
Conclusion:
From the above analysis, we can conclude that R is reflexive, but neither symmetric nor transitive. Therefore, the correct answer is option C.
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If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, but neither symmetric nor transitived)R is reflexive, symmetric and transitiveCorrect answer is option 'C'. Can you explain this answer?
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If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, but neither symmetric nor transitived)R is reflexive, symmetric and transitiveCorrect answer is option 'C'. 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 If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, but neither symmetric nor transitived)R is reflexive, symmetric and transitiveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, but neither symmetric nor transitived)R is reflexive, symmetric and transitiveCorrect answer is option 'C'. Can you explain this answer?.
If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, but neither symmetric nor transitived)R is reflexive, symmetric and transitiveCorrect answer is option 'C'. 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 If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, but neither symmetric nor transitived)R is reflexive, symmetric and transitiveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A - {a, b, c} and R - {(a, a), (a, b) ( b, c), (b, b), (c, c), (c, a)} is a binary relation on A, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, but neither symmetric nor transitived)R is reflexive, symmetric and transitiveCorrect answer is option 'C'. Can you explain this answer?.
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