For R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,4),(4,2)} on A={1,2,3,4}, which missing ordered pair directly witnesses that R is not transitive?
Answer and explanation
Correct answer: (1,4)
We have (1,2)∈R and (2,4)∈R. Transitivity would therefore require (1,4)∈R, but that pair is absent. This gives a direct counterexample. The relation is also symmetric because the reverse pairs are present, but symmetry does not supply the missing transitive pair. In fact, adding both (1,4) and (4,1) would be needed to complete the corresponding equivalence block.
Frequently asked questions
What is the correct answer to this question?
(1,4)
Why is this the correct answer?
We have (1,2)∈R and (2,4)∈R. Transitivity would therefore require (1,4)∈R, but that pair is absent. This gives a direct counterexample. The relation is also symmetric because the reverse pairs are present, but symmetry does not supply the missing transitive pair. In fact, adding both (1,4) and (4,1) would be needed to complete the corresponding equivalence block.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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