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Class 12MathematicsRelations and FunctionsIntroduction to RelationsExpert
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On (A={1,2,3,4}), which new pair is minimally needed to make (R={(1,2),(2,3),(4,4)}) transitive?

Answer and explanation

Correct answer: ((1,3))

Step 1: ((1,2)) and ((2,3)) require ((1,3)) for transitivity. Step 2: ((4,4)) only requires itself, which is already present. Step 3: Hence the minimal new pair is ((1,3)).

Related tags

RelationsTransitive-ClosureMinimal-AdditionClass12Introduction 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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