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Subjects
Class 12MathematicsRelations and FunctionsIntroduction to RelationsHard
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On (A={1,2,3,4}), if (aRb) when (a+b=5), why is (R) not transitive?

Answer and explanation

Correct answer: Because ((1,4)) and ((4,1)) are present but ((1,1)) is not

Step 1: Since (1+4=5), ((1,4)) and ((4,1)) are in the relation. Step 2: Transitivity would require ((1,1)). Step 3: ((1,1)) is absent because (1+1\ne5), so transitivity fails.

Related tags

RelationsNot TransitiveSum RelationIntroduction To RelationsRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1If (A={1,2}), what does a relation on (A) mean?
  2. 2If (A={a,b}) and (B={1,2}), how many ordered pairs are there in (A\times B)?
  3. 3If (A={1,2}), how many total relations can be formed on (A)?
  4. 4Which relation is the universal relation on (A={1,2,3})?
  5. 5Which statement is correct about the empty relation?
  6. 6If (A={1,2,3}), how many pairs are there in the universal relation on (A)?
  7. 7Which pairs are compulsory in the identity relation on a set (A)?
  8. 8If (A={1,2,3}), which is the identity relation?
  9. 9What condition is necessary for a relation (R) to be reflexive?
  10. 10On (A={1,2}), which property is definitely satisfied by (R={(1,1),(2,2),(1,2)})?
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