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Subjects
Class 12MathematicsRelations and FunctionsTransitive relationEasyLevel 13

Is the empty relation (\varnothing) on a set (A) transitive or not?

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Answer and explanation

Correct answer: Transitive

Step 1: The transitive condition is checked only when both ((a,b)) and ((b,c)) are present. Step 2: The empty relation has no pair, so no example violates the condition. Step 3: Remember that the empty relation is transitive by vacuous truth.

Tags

transitive relationempty relationvacuous truth

Frequently asked questions

What is the correct answer to this question?

Transitive

Why is this the correct answer?

Step 1: The transitive condition is checked only when both ((a,b)) and ((b,c)) are present. Step 2: The empty relation has no pair, so no example violates the condition. Step 3: Remember that the empty relation is transitive by vacuous truth.

Which subject and chapter does this question cover?

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

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10 more MCQs
  1. 1Which is the correct definition of a transitive relation?
  2. 2On (A={1,2,3}), (R={(1,2),(2,3),(1,3)}) is given. Is (R) transitive?
  3. 3On (A={1,2,3}), (R={(1,2),(2,3)}). Why is (R) not transitive?
  4. 4On natural numbers, relation (R) is defined by (aRb) if (a\le b). What is (R)?
  5. 5On real numbers, (R={(a,b):a<b}). Is (R) transitive?
  6. 6On (A={1,2,3}), (R={(1,1),(2,2),(3,3)}) is given. Choose the correct statement about (R).
  7. 7Why is the universal relation (A\times A) on a set (A) transitive?
  8. 8On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4)}). Is (R) transitive or not?
  9. 9On (A={1,2,3,4}), which pair must be added to make (R={(1,2),(2,4)}) transitive?
  10. 10On integers, relation (R) is defined by (aRb) if (a=b). What type of relation is it?
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