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Subjects
Class 12MathematicsRelations and FunctionsTransitive relationEasyLevel 13

Why is the universal relation (A\times A) on a set (A) transitive?

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Answer and explanation

Correct answer: Because every required pair is already present

Step 1: (A\times A) contains all possible ordered pairs from (A). Step 2: If ((a,b)) and ((b,c)) are present, then ((a,c)) is also surely present. Step 3: A relation with all possible pairs automatically satisfies transitivity.

Tags

transitive relationuniversal relationcartesian product

Frequently asked questions

What is the correct answer to this question?

Because every required pair is already present

Why is this the correct answer?

Step 1: (A\times A) contains all possible ordered pairs from (A). Step 2: If ((a,b)) and ((b,c)) are present, then ((a,c)) is also surely present. Step 3: A relation with all possible pairs automatically satisfies transitivity.

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. 7Is the empty relation (\varnothing) on a set (A) transitive or not?
  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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