On A={1,2,3}, let R={(1,2),(2,1),(1,1),(2,2)}. Is R transitive?
Answer and explanation
Correct answer: Yes
Transitivity concerns only pairs that can be joined through a common middle element. The chain (1,2),(2,1) requires (1,1), which is present; the reverse chain (2,1),(1,2) requires (2,2), also present. Chains involving 1,1 or 2,2 reproduce already listed pairs. Element 3 appears in no pair, so no pair involving 3 is required. Thus R is transitive, making A correct.
Frequently asked questions
What is the correct answer to this question?
Yes
Why is this the correct answer?
Transitivity concerns only pairs that can be joined through a common middle element. The chain (1,2),(2,1) requires (1,1), which is present; the reverse chain (2,1),(1,2) requires (2,2), also present. Chains involving 1,1 or 2,2 reproduce already listed pairs. Element 3 appears in no pair, so no pair involving 3 is required. Thus R is transitive, making A correct.
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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