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Class 12MathematicsRelations and FunctionsIntroduction to RelationsExpert
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On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}) and (S={(a,b):a-b\text{ is divisible by }4}). How many pairs are in (R\cap S)?

Answer and explanation

Correct answer: (4)

Step 1: In this set, (a-b) being divisible by (4) occurs only for equal elements. Step 2: So (S) acts like the identity relation, and all its (4) self-pairs also lie in (R). Step 3: Hence (R\cap S) contains (4) pairs.

Related tags

IntersectionModular-RelationCountingIntroduction To RelationsRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1If (A={1,2}), what does a relation on (A) mean?
  2. 2If (A={a,b}) and (B={1,2}), how many ordered pairs are there in (A\times B)?
  3. 3If (A={1,2}), how many total relations can be formed on (A)?
  4. 4Which relation is the universal relation on (A={1,2,3})?
  5. 5Which statement is correct about the empty relation?
  6. 6If (A={1,2,3}), how many pairs are there in the universal relation on (A)?
  7. 7Which pairs are compulsory in the identity relation on a set (A)?
  8. 8If (A={1,2,3}), which is the identity relation?
  9. 9What condition is necessary for a relation (R) to be reflexive?
  10. 10On (A={1,2}), which property is definitely satisfied by (R={(1,1),(2,2),(1,2)})?
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