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Class 12MathematicsRelations and FunctionsReflexive relationMediumLevel 9
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On A = {1, 2, 3}, let R = (A × A) \ {(1, 2), (2, 3)}. What is R?

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Answer and explanation

Correct answer: Reflexive

A × A initially contains every ordered pair of A, including all diagonal pairs (1, 1), (2, 2), and (3, 3). The two removed pairs, (1, 2) and (2, 3), are off-diagonal pairs; neither is of the form (a, a). Therefore all required self-pairs remain in R, so R is reflexive. Removing some non-self-pairs does not destroy reflexivity. The relation is not empty and is much larger than the identity relation, making option A correct.

Related tags

Reflexive RelationUniversal RelationDiagonal Pairs

Frequently asked questions

What is the correct answer to this question?

Reflexive

Why is this the correct answer?

A × A initially contains every ordered pair of A, including all diagonal pairs (1, 1), (2, 2), and (3, 3). The two removed pairs, (1, 2) and (2, 3), are off-diagonal pairs; neither is of the form (a, a). Therefore all required self-pairs remain in R, so R is reflexive. Removing some non-self-pairs does not destroy reflexivity. The relation is not empty and is much larger than the identity relation, making option A correct.

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.

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