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Class 12MathematicsRelations and FunctionsIntroduction to RelationsHard
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If (R) is symmetric on (A={1,2,3}) and ((1,3)) is in (R\circ R), what type of chain may be possible?

Answer and explanation

Correct answer: For some (b), ((1,b)\in R) and ((b,3)\in R)

Step 1: Composition (R\circ R) is checked through a chain of two pairs. Step 2: For ((1,3)) to appear, there must be some middle element (b) with (1) related to (b) and (b) related to (3). Step 3: In composition questions, look for the middle element.

Related tags

RelationsCompositionChain ConditionIntroduction 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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