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Class 12MathematicsRelations and FunctionsReflexive relationMediumLevel 9

On A = {1, 2, 3}, let R = (A × A) \ {(2, 2)}. Which statement about R is correct?

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Answer and explanation

Correct answer: R is not reflexive

The Cartesian product A × A contains every ordered pair from A, including the three self-pairs (1, 1), (2, 2), and (3, 3). The relation R is obtained by deleting (2, 2), so although (1, 1) and (3, 3) remain, the required self-pair for 2 is missing. Reflexivity requires all self-pairs, not merely most of them. Therefore R is not reflexive. It is neither the identity relation nor empty, so option B is correct.

Tags

reflexive relationCartesian productmissing self-pair

Frequently asked questions

What is the correct answer to this question?

R is not reflexive

Why is this the correct answer?

The Cartesian product A × A contains every ordered pair from A, including the three self-pairs (1, 1), (2, 2), and (3, 3). The relation R is obtained by deleting (2, 2), so although (1, 1) and (3, 3) remain, the required self-pair for 2 is missing. Reflexivity requires all self-pairs, not merely most of them. Therefore R is not reflexive. It is neither the identity relation nor empty, so option B is 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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