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Class 12MathematicsRelations and FunctionsIntroduction to RelationsExpert
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For (R={(1,2),(2,3),(3,4)}) on (A={1,2,3,4}), how many minimum pairs must be added to form the transitive closure?

Answer and explanation

Correct answer: (3)

Step 1: ((1,2)) and ((2,3)) require ((1,3)). Step 2: ((2,3)) and ((3,4)) require ((2,4)). Step 3: Then ((1,3)) and ((3,4)) require ((1,4)), so (3) pairs are needed.

Related tags

RelationsTransitive-ClosureOrdered-PairsExpertIntroduction 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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