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Class 12MathematicsRelations and FunctionsReflexive relationHard
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What is the smallest necessary extension that makes a relation (R) reflexive?

Answer and explanation

Correct answer: (R \cup \Delta_A)

Step 1: (\Delta_A={(a,a):a \in A}) contains all diagonal pairs. Step 2: (R \cup \Delta_A) keeps the old pairs and adds any missing diagonal pairs. Step 3: This gives the smallest reflexive closure.

Related tags

RelationsFunctionsReflexive RelationReflexive ClosureHardReflexive 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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