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Subjects
Class 12MathematicsRelations and FunctionsIntroduction to RelationsMedium
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If (A={1,2,3}) and (R={(1,2),(3,3)}), what is the smallest relation needed to make (R) symmetric?

Answer and explanation

Correct answer: ({(1,2),(2,1),(3,3)})

Step 1: For symmetry, the reverse ((2,1)) of ((1,2)) must be added. Step 2: ((3,3)) is its own reverse, so no extra pair is needed for it. Step 3: For the smallest relation add only compulsory pairs.

Related tags

RelationsSymmetric-ClosureSmallest-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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