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Class 12MathematicsRelations and FunctionsIntroduction to RelationsHard
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If (R={(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), why is (R) symmetric but not an equivalence relation?

Answer and explanation

Correct answer: Because reflexivity is absent

Step 1: Every pair has its reverse, so it is symmetric. Step 2: ((1,1)), ((2,2)), and ((3,3)) are absent, so reflexivity is missing. Step 3: An equivalence relation needs reflexivity, symmetry and transitivity.

Related tags

RelationsSymmetric Not EquivalenceReflexivityIntroduction 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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