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Subjects
Class 11MathematicsRelations and FunctionsCartesian product of setsMediumLevel 26
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If A = {1,2,3} and R = A×A, what type of relation is R?

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Answer and explanation

Correct answer: Universal relation

By definition, A×A is the set of every ordered pair (a,b) in which both a and b belong to A. Since R is exactly A×A, it contains all 3×3 = 9 possible ordered pairs, including every diagonal and every reverse pair. A relation containing every pair from A×A is called the universal relation. Therefore option B is correct; it is not empty, not merely the identity relation, and it is not asymmetric.

Related tags

RelationsCartesian ProductUniversal Relation

Frequently asked questions

What is the correct answer to this question?

Universal relation

Why is this the correct answer?

By definition, A×A is the set of every ordered pair (a,b) in which both a and b belong to A. Since R is exactly A×A, it contains all 3×3 = 9 possible ordered pairs, including every diagonal and every reverse pair. A relation containing every pair from A×A is called the universal relation. Therefore option B is correct; it is not empty, not merely the identity relation, and it is not asymmetric.

Which subject and chapter does this question cover?

This is a Class 11 Mathematics question. Chapter: Relations and Functions. Topic: Cartesian product of sets.

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10 more MCQs
  1. 1If (A) and (B) are two sets, what is the correct meaning of (A\times B)?
  2. 2If A = {1, 2} and B = {3}, what is A × B?
  3. 3If (A={5}) and (B={7,8}), how many ordered pairs are in (A×B)?
  4. 4If (n(A)=4) and (n(B)=5), what is (n(A\times B))?
  5. 5If (A=\varnothing) and (B={1,2}), what is (A\times B)?
  6. 6If (A={1,2}) and (B={3,4}), is ((2,3)\in A\times B)?
  7. 7If ((p,q)\in A\times B), which statement is always true?
  8. 8Generally, which statement about (A\times B) and (B\times A) is correct?
  9. 9If (A={1}) and (B={1,2}), which statement is correct?
  10. 10In the ordered pair ((5,7)), what is the first component?
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