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Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R is
- a)reflexive only
- b)symmetric only
- c)transitive only
- d)an equivalence relation
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let R be a relation over the set N x N and it is defined by (a, b)R (c...
We have (a,b) R (a, b) for all (a, b) ∈ N x N
Since. a + b = b + a.
Hence, R is reflexive.
R is symmetric for we have (a , b) R (c, d)
implies a + d = b + c
implies d + a = c + b
implies c + b = d + a
implies (c, d) R (e, f)
Then, by definition of R,
we have a + d = b + c and c + f = d + e when by addition, we get
a + d + c + f = b + c + d + e
or a + f = b + e
Hence, (a, b) R (e , f)
Thus, (a, b) R( c, d) and (c, d) R (e , f) implies (a , b) R (e , f)
Since. a + b = b + a.
Hence, R is reflexive.
R is symmetric for we have (a , b) R (c, d)
implies a + d = b + c
implies d + a = c + b
implies c + b = d + a
implies (c, d) R (e, f)
Then, by definition of R,
we have a + d = b + c and c + f = d + e when by addition, we get
a + d + c + f = b + c + d + e
or a + f = b + e
Hence, (a, b) R (e , f)
Thus, (a, b) R( c, d) and (c, d) R (e , f) implies (a , b) R (e , f)
Most Upvoted Answer
Let R be a relation over the set N x N and it is defined by (a, b)R (c...
We have (a,b) R (a, b) for all (a, b) ∈ N x N
Since. a + b = b + a.
Hence, R is reflexive.
R is symmetric for we have (a , b) R (c, d)
implies a + d = b + c
implies d + a = c + b
implies c + b = d + a
implies (c, d) R (e, f)
Then, by definition of R,
we have a + d = b + c and c + f = d + e when by addition, we get
a + d + c + f = b + c + d + e
or a + f = b + e
Hence, (a, b) R (e , f)
Thus, (a, b) R( c, d) and (c, d) R (e , f) implies (a , b) R (e , f)
Since. a + b = b + a.
Hence, R is reflexive.
R is symmetric for we have (a , b) R (c, d)
implies a + d = b + c
implies d + a = c + b
implies c + b = d + a
implies (c, d) R (e, f)
Then, by definition of R,
we have a + d = b + c and c + f = d + e when by addition, we get
a + d + c + f = b + c + d + e
or a + f = b + e
Hence, (a, b) R (e , f)
Thus, (a, b) R( c, d) and (c, d) R (e , f) implies (a , b) R (e , f)
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Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer?
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Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. 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 Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer?.
Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. 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 Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Let R be a relation over the set N x N and it is defined by (a, b)R (c, d) ⇒ a + d = b + c. Then R isa)reflexive onlyb)symmetric onlyc)transitive onlyd)an equivalence relationCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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