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Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5}), the classes of (R) are ({1,3,5}) and ({2,4}). How many pairs will be in (R)?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), the equivalence classes of (R) are ({1,2}) and ({3,4}). How many ordered pairs are in (R)?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5,6}), (aRb) if and only if (a\equiv b \pmod{3}). What is the equivalence class of (1)?
Class 12 · Mathematics · Expert
→If (A={1,2,3,4}), what is the ratio of the number of reflexive relations to the number of all relations on (A)?
Class 12 · Mathematics · Expert
→If (A) has (n) elements, which is the number of symmetric relations on (A)?
Class 12 · Mathematics · Expert
→Let |A|=5. A relation R on A is reflexive and symmetric and is required to contain (1,2). How many such relations are possible?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), (aRb) if and only if (a=b) or (a+b=5). Choose the correct conclusion.
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), (aRb) if and only if (a+b=5). Choose the correct type of the relation.
Class 12 · Mathematics · Expert
→On real numbers, (aRb) if and only if (a-b) is irrational. What is the correct conclusion?
Class 12 · Mathematics · Expert
→On real numbers, (aRb) if and only if (a-b) is rational. Choose the correct classification.
Class 12 · Mathematics · Expert
→On real numbers, (aRb) if and only if (a^2=b^2). What type of relation is it?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5}), (aRb) if and only if (|a-b|\le2). Choose the correct statement.
Class 12 · Mathematics · Expert
→On integers, (aRb) if and only if (a-b) is divisible by (7). Choose the correct conclusion.
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,6}), (aRb) if and only if (a\mid b). What type of relation is it?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), the relation (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(1,3),(3,4),(1,4)}) is given. Choose the correct classification.
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R) is an equivalence relation with classes ({1,3}) and ({2,4}). How many ordered pairs are in (R)?
Class 12 · Mathematics · Hard
→If (A={1,2,3,4,5}) and (R) is a reflexive relation, what is the minimum number of pairs in (R)?
Class 12 · Mathematics · Hard
→If (A={1,2,3,4}) and (R) is a reflexive relation, what is the maximum number of pairs in (R)?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)}). Which statement is correct?
Class 12 · Mathematics · Hard
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