If A={1,2,3} and R={(1,2),(2,3),(1,3)}, which fact shows the transitive property?
Answer and explanation
Correct answer: (1,2) and (2,3) imply (1,3)
The governing definition of transitivity is: if (a,b)∈R and (b,c)∈R, then (a,c) must also belong to R. In the given relation, (1,2) and (2,3) are both present. They form a chain because the second coordinate of the first pair, 2, equals the first coordinate of the second pair. The transitive conclusion is therefore (1,3), and this pair is indeed included in R. Hence option A correctly demonstrates the property. The presence of (1,1), (3,1), or (2,2) alone does not show the required implication; such facts may concern other relation properties, but they do not establish transitivity.
Frequently asked questions
What is the correct answer to this question?
(1,2) and (2,3) imply (1,3)
Why is this the correct answer?
The governing definition of transitivity is: if (a,b)∈R and (b,c)∈R, then (a,c) must also belong to R. In the given relation, (1,2) and (2,3) are both present. They form a chain because the second coordinate of the first pair, 2, equals the first coordinate of the second pair. The transitive conclusion is therefore (1,3), and this pair is indeed included in R. Hence option A correctly demonstrates the property. The presence of (1,1), (3,1), or (2,2) alone does not show the required implication; such facts may concern other relation properties, but they do not establish transitivity.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Transitive relation.
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