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Subjects
Class 12MathematicsRelations and FunctionsTypes of relationsExpertLevel 4
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For the relation defined by aRb iff a=b or both a and b are greater than 2 on A={1,2,3,4}, what is the equivalence class of 3?

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Answer and explanation

Correct answer: {3,4}

The element 3 is related to itself by the equality condition. It is also related to 4 because both 3 and 4 are greater than 2. It is not related to 1 or 2, since they are unequal to 3 and are not both greater than 2. Therefore the equivalence class containing 3 is {3,4}. Option A omits the valid pair with 4, while B and D include elements that do not satisfy the definition.

Related tags

Equivalence RelationEquivalence ClassPartitionRelations

Frequently asked questions

What is the correct answer to this question?

{3,4}

Why is this the correct answer?

The element 3 is related to itself by the equality condition. It is also related to 4 because both 3 and 4 are greater than 2. It is not related to 1 or 2, since they are unequal to 3 and are not both greater than 2. Therefore the equivalence class containing 3 is {3,4}. Option A omits the valid pair with 4, while B and D include elements that do not satisfy the definition.

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.

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10 more MCQs
  1. 1What is the relation on a set (A) called when it contains all ordered pairs of (A\times A)?
  2. 2What is the relation on a non-empty set (A) called when it has no ordered pair?
  3. 3What is the relation on (A) called when it contains only pairs of the form ((a,a))?
  4. 4When is a relation (R) on a set (A) called reflexive?
  5. 5Which condition is necessary for a relation (R) to be symmetric?
  6. 6Which condition is correct for a relation (R) to be transitive?
  7. 7Which three properties are needed for a relation to be an equivalence relation?
  8. 8Which properties are needed for a relation to be a partial order relation?
  9. 9On A={1,2,3}, let R={(1,2),(2,1)}. Which is the most accurate description of R?
  10. 10On (A={1,2}), what type of relation is (R=A\times A)?
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