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Class 12 · Mathematics · Expert
→If (A=\mathcal{P}({1,2})) and (R={(X,Y):X\triangle Y=X}), how many diagonal pairs are in (R)?
Class 12 · Mathematics · Hard
→If (R) is reflexive on (A), which statement about (R\cup R^{-1}) is always true?
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R) is reflexive and symmetric and has 12 total pairs. How many such relations are possible?
Class 12 · Mathematics · Hard
→If (R) is reflexive on (A), what can certainly be said about (R^{-1}\cap R)?
Class 12 · Mathematics · Expert
→If (S={1,2,3}) and (A=\mathcal{P}(S)). On (A), (R={(X,Y):X\triangle Y=\varnothing}). Choose the correct statement about (R).
Class 12 · Mathematics · Hard
→On (A={1,2,3,4}), (R) is reflexive and symmetric and has total 8 pairs. How many such relations are possible?
Class 12 · Mathematics · Hard
→On (A={1,2,3}), (R) is reflexive and symmetric and has total 7 pairs. How many such relations are possible?
Class 12 · Mathematics · Hard
→How many relations on a three-element set are both reflexive and antisymmetric?
Class 12 · Mathematics · Hard
→How many relations on a four-element set are both reflexive and symmetric?
Class 12 · Mathematics · Expert
→If (R) is not symmetric, choose the correct statement about (R\cup R^{-1}).
Class 12 · Mathematics · Expert
→For any relation (R), which statement about (R\cup R^{-1}) is always true?
Class 12 · Mathematics · Expert
→For any relation (R), which statement about (R\cap R^{-1}) is always true?
Class 12 · Mathematics · Expert
→If (R) is a symmetric relation on a set, choose the correct statement about (R\cup R^{-1}).
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5}), (aRb) if and only if (a+b\le6). Choose the correct statement.
Class 12 · Mathematics · Expert
→On real numbers, (aRb) if and only if (a^2+b^2=1). Choose the correct classification.
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5}), (aRb) if and only if (a) and (b) have different remainders when divided by (2). What type of relation is it?
Class 12 · Mathematics · Expert
→On real numbers, (aRb) if and only if (a-b=2). Choose the correct classification.
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5}), (aRb) if and only if (|a-b|=2). Choose the correct statement.
Class 12 · Mathematics · Expert
→If (R) is symmetric and transitive, is (R) always reflexive? Choose the correct option.
Class 12 · Mathematics · Expert
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