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Subjects
Class 12MathematicsRelations and FunctionsEquivalence relationHardLevel 17
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On the integers, aRb when a-b is divisible by 5, and aSc when a-c is divisible by 10. What is R∪S equal to?

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Answer and explanation

Correct answer: Congruence modulo 5

Relation R consists of integer pairs whose difference is a multiple of 5, while S consists of pairs whose difference is a multiple of 10. Every multiple of 10 is also a multiple of 5, so S is a subset of R. The union of a relation with its subset is the larger relation itself: R∪S=R. Therefore the union is congruence modulo 5, making option A correct; modulo 10 would describe S, not the union.

Related tags

Equivalence RelationUnion Of RelationsCongruence Modulo 5

Frequently asked questions

What is the correct answer to this question?

Congruence modulo 5

Why is this the correct answer?

Relation R consists of integer pairs whose difference is a multiple of 5, while S consists of pairs whose difference is a multiple of 10. Every multiple of 10 is also a multiple of 5, so S is a subset of R. The union of a relation with its subset is the larger relation itself: R∪S=R. Therefore the union is congruence modulo 5, making option A correct; modulo 10 would describe S, not the union.

Which subject and chapter does this question cover?

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

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10 more MCQs
  1. 1Which three properties must a relation have to be an equivalence relation?
  2. 2Why is the universal relation on (A={1,2,3}) always reflexive?
  3. 3Why is the empty relation on (A={1,2,3}) not an equivalence relation?
  4. 4If (R) is an equivalence relation and ((a,b)\in R), ((b,c)\in R), which conclusion is correct?
  5. 5On integers, (aRb) if (a-b) is even. What kind of relation is this?
  6. 6On integers, (aRb) if (a\equiv b \pmod{3}). How many equivalence classes are there?
  7. 7For a relation (aRb) if (a=b), what type of relation is it on any set?
  8. 8On (A={1,2,3}), (R=A\times A). What kind of relation is it?
  9. 9If ((a,a)\in R) for every (a\in A), which property is this?
  10. 10If ((a,b)\in R) always implies ((b,a)\in R), which property is this?
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