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Subjects
Class 12MathematicsRelations and FunctionsSymmetric relationMediumLevel 12
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If R and S are both symmetric relations, what is the correct statement about R ∪ S?

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Answer and explanation

Correct answer: R ∪ S will be symmetric

Suppose (a,b) belongs to R ∪ S. Then it belongs to at least one of R or S. If it belongs to R, symmetry of R gives (b,a) ∈ R; if it belongs to S, symmetry of S gives (b,a) ∈ S. In either case, (b,a) belongs to the union. Therefore R ∪ S is symmetric, while the other options make unnecessarily restrictive claims.

Related tags

Union Of RelationsSymmetric RelationSet Operations

Frequently asked questions

What is the correct answer to this question?

R ∪ S will be symmetric

Why is this the correct answer?

Suppose (a,b) belongs to R ∪ S. Then it belongs to at least one of R or S. If it belongs to R, symmetry of R gives (b,a) ∈ R; if it belongs to S, symmetry of S gives (b,a) ∈ S. In either case, (b,a) belongs to the union. Therefore R ∪ S is symmetric, while the other options make unnecessarily restrictive claims.

Which subject and chapter does this question cover?

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

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10 more MCQs
  1. 1On the set (A={1,2,3}), the relation (R={(1,2),(2,1),(3,3)}) is given. What type of relation is it?
  2. 2If a relation (R) contains ((4,7)) and (R) is symmetric, which ordered pair must definitely be in (R)?
  3. 3On (A={1,2}), (R={(1,1),(1,2)}) is given. Which pair must be added to make it symmetric?
  4. 4Which statement correctly identifies a symmetric relation?
  5. 5On the set (A={1,2,3}), which relation is not symmetric?
  6. 6If (R={(2,2),(3,5),(5,3)}), which statement about (R) is correct?
  7. 7On (A={1,2,3}), (R={(1,2),(2,1),(2,3)}). Why is (R) not symmetric?
  8. 8Is the empty relation (R=\varnothing) on a non-empty set (A) symmetric or not?
  9. 9Is the universal relation (R=A \times A) on a set (A) symmetric or not?
  10. 10On (A={1,2,3}), (R={(1,1),(2,2),(3,3)}). Why is this relation symmetric?
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