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Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false?
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Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a ...
Answer:
Transitive Relation:
A relation R on a set A is said to be transitive if (a, b) ∈ R and (b, c) ∈ R imply (a, c) ∈ R for any a, b, c ∈ A.
Given Relation:
A={1,2,3}
R={(1,2) , (1,3)}
Checking for Transitivity:
To check the transitivity of R, we need to check whether (1,2) and (2,3) belongs to R or not. If (1,2) and (2,3) belongs to R, then (1,3) should also belongs to R for R to be transitive.
But, (1,2) ∈ R and (2,3) ∉ R. Therefore, R is not transitive.
Conclusion:
The given relation R is not transitive.
Transitive Relation:
A relation R on a set A is said to be transitive if (a, b) ∈ R and (b, c) ∈ R imply (a, c) ∈ R for any a, b, c ∈ A.
Given Relation:
A={1,2,3}
R={(1,2) , (1,3)}
Checking for Transitivity:
To check the transitivity of R, we need to check whether (1,2) and (2,3) belongs to R or not. If (1,2) and (2,3) belongs to R, then (1,3) should also belongs to R for R to be transitive.
But, (1,2) ∈ R and (2,3) ∉ R. Therefore, R is not transitive.
Conclusion:
The given relation R is not transitive.
Community Answer
Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a ...
True. bcz (a, b) €R and ( b, c) is not present therefore it is transitive relation [ if (b, c) €R therefore (c, a) €R is important but now it doesn't matter].
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Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false?
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Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false?.
Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the set A={1,2,3} and the relation R={(1,2) , (1,3)}. R is a transitive relation . State true or false?.
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