On A={1,2,3,4}, let R={(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}. What is the nature of R?
Answer and explanation
Correct answer: Transitive
The relation contains every pair needed from the displayed increasing chains. Specifically, (1,2) and (2,3) give (1,3); (2,3) and (3,4) give (2,4); and (1,3) and (3,4) give (1,4). Other composable pairs either repeat these requirements or have no matching middle element. Therefore every transitivity implication is satisfied. The relation need not be reflexive or symmetric to be transitive, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Transitive
Why is this the correct answer?
The relation contains every pair needed from the displayed increasing chains. Specifically, (1,2) and (2,3) give (1,3); (2,3) and (3,4) give (2,4); and (1,3) and (3,4) give (1,4). Other composable pairs either repeat these requirements or have no matching middle element. Therefore every transitivity implication is satisfied. The relation need not be reflexive or symmetric to be transitive, so option A is 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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