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Subjects
Class 12MathematicsRelations and FunctionsReflexive relationHard
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What is the smallest reflexive relation on a set (A)?

Answer and explanation

Correct answer: Identity relation (\Delta_A={(a,a):a \in A})

Step 1: Reflexivity requires all diagonal pairs. Step 2: The smallest relation keeps only those compulsory pairs and no extra pair. Step 3: Therefore the identity relation is the smallest reflexive relation.

Related tags

RelationsFunctionsReflexive RelationIdentity RelationHardReflexive RelationRelations And FunctionsMathematics
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10 more MCQs
  1. 1Which relation is reflexive on A={1,2,3}?
  2. 2For a set A with 3 elements, how many relations are not reflexive?
  3. 3What is the correct identification of a reflexive relation?
  4. 4If (A={1,2,3}), which pairs are compulsory for a reflexive relation on (A)?
  5. 5Let (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2)}). What type of relation is (R)?
  6. 6Let (A={1,2,3}) and (R={(1,1),(2,2),(1,3)}). Why is (R) not reflexive?
  7. 7If (A) has 4 elements, what is the minimum number of pairs in a reflexive relation on (A)?
  8. 8If (A={a,b,c,d}), which is the minimum reflexive relation?
  9. 9On a non-empty set (A), what kind of relation is the universal relation (A \times A)?
  10. 10Why is the empty relation (\varnothing) not reflexive on a non-empty set (A)?
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