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Class 12MathematicsRelations and FunctionsTransitive relationEasy
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If (R={(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}), what is the correct statement about (R)?

Answer and explanation

Correct answer: It is transitive

Step 1: ((1,2)) with ((2,3)) requires ((1,3)), and ((2,3)) with ((3,4)) requires ((2,4)). Step 2: ((1,3)) with ((3,4)) also requires ((1,4)), which is present. Step 3: In step-like relations, check both short and long jumps.

Related tags

Transitive RelationChain ClosureClass 12RelationsRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1Which transitivity requirement fails for R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4)} on A={1,2,3,4}?
  2. 2On A={1,2,3}, what is the smallest addition to R={(1,2),(2,3)} that makes R transitive?
  3. 3If R and S are transitive relations on the same set, which statement about their union R∪S is always valid?
  4. 4For 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?
  5. 5Which relation on A={1,2,3} is transitive but not symmetric?
  6. 6If R and S are transitive relations on A, which implication proves that R∩S is transitive?
  7. 7Which pair of transitive relations gives a union that is not transitive?
  8. 8Which is the correct definition of a transitive relation?
  9. 9On (A={1,2,3}), (R={(1,2),(2,3),(1,3)}) is given. Is (R) transitive?
  10. 10On (A={1,2,3}), (R={(1,2),(2,3)}). Why is (R) not transitive?
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