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For a, b ε Z, define a relation a R b if ab > 0. Then the relation R is
- a)symmetric, reflexive and transitive
- b)symmetric and reflexive but NOT transitive
- c)symmetric and transitive but NOT reflexive
- d)reflexive and transitive nut NOT symmetric
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
For a, b ε Z, define a relation a R b if ab > 0. Then the r...
For a, b ε z, define a relation aRb if ab ≥ 0 then the relation R is an equivalence relation.
Hence, the relation R is symmetric, reflexive and transitive.
Hence, the relation R is symmetric, reflexive and transitive.
Most Upvoted Answer
For a, b ε Z, define a relation a R b if ab > 0. Then the r...
Reflexive Property:
For a relation to be reflexive, every element in the set must be related to itself. In this case, since a * a = a^2 is always greater than 0 for any non-zero integer a, the relation is reflexive.
Symmetric Property:
For a relation to be symmetric, if a is related to b, then b must be related to a. In this case, if a * b > 0, then b * a > 0 as well. Therefore, the relation is symmetric.
Transitive Property:
For a relation to be transitive, if a is related to b and b is related to c, then a must be related to c. In this case, if a * b > 0 and b * c > 0, then a * c > 0. Therefore, the relation is transitive.
Therefore, the relation R is reflexive, symmetric, and transitive, making the correct answer option 'A'.
For a relation to be reflexive, every element in the set must be related to itself. In this case, since a * a = a^2 is always greater than 0 for any non-zero integer a, the relation is reflexive.
Symmetric Property:
For a relation to be symmetric, if a is related to b, then b must be related to a. In this case, if a * b > 0, then b * a > 0 as well. Therefore, the relation is symmetric.
Transitive Property:
For a relation to be transitive, if a is related to b and b is related to c, then a must be related to c. In this case, if a * b > 0 and b * c > 0, then a * c > 0. Therefore, the relation is transitive.
Therefore, the relation R is reflexive, symmetric, and transitive, making the correct answer option 'A'.
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Community Answer
For a, b ε Z, define a relation a R b if ab > 0. Then the r...
For a, b ε z, define a relation aRb if ab ≥ 0 then the relation R is an equivalence relation.
Hence, the relation R is symmetric, reflexive and transitive.
Hence, the relation R is symmetric, reflexive and transitive.
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For a, b ε Z, define a relation a R b if ab > 0. Then the relation R isa)symmetric, reflexive and transitiveb)symmetric and reflexive but NOT transitivec)symmetric and transitive but NOT reflexived)reflexive and transitive nut NOT symmetricCorrect answer is option 'A'. Can you explain this answer?
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For a, b ε Z, define a relation a R b if ab > 0. Then the relation R isa)symmetric, reflexive and transitiveb)symmetric and reflexive but NOT transitivec)symmetric and transitive but NOT reflexived)reflexive and transitive nut NOT symmetricCorrect answer is option 'A'. 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 For a, b ε Z, define a relation a R b if ab > 0. Then the relation R isa)symmetric, reflexive and transitiveb)symmetric and reflexive but NOT transitivec)symmetric and transitive but NOT reflexived)reflexive and transitive nut NOT symmetricCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a, b ε Z, define a relation a R b if ab > 0. Then the relation R isa)symmetric, reflexive and transitiveb)symmetric and reflexive but NOT transitivec)symmetric and transitive but NOT reflexived)reflexive and transitive nut NOT symmetricCorrect answer is option 'A'. Can you explain this answer?.
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