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Class 12 · Mathematics
→If (R) is symmetric and transitive, is (R) always reflexive? Choose the correct option.
Class 12 · Mathematics
→If (R) is reflexive and transitive, which statement is always true about (R^{-1})?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,2),(2,1),(2,3),(3,2),(3,4),(4,3)}). Which pair must necessarily appear when making it transitive?
Class 12 · Mathematics
→On (A={1,2,3}), what is the smallest symmetric extension of (R={(1,2),(2,1),(2,3)})?
Class 12 · Mathematics
→On (A={1,2,3,4}), what is the transitive closure of (R={(1,2),(2,3),(3,4)})?
Class 12 · Mathematics
→Which pair of transitive relations gives a union that is not transitive?
Class 12 · Mathematics
→If R and S are transitive relations on A, which implication proves that R∩S is transitive?
Class 12 · Mathematics
→If (R) and (S) are reflexive relations, choose the correct statement about (R\cup S).
Class 12 · Mathematics
→If (R) and (S) are symmetric relations, which statement about (R\cap S) is correct?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)}). How many equivalence classes does (R) have?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if (a\equiv b \pmod{2}) and (a\equiv b \pmod{3}). Choose the correct conclusion.
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a^2-b^2\ge0). Choose the correct statement.
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). How many ordered pairs are in the relation?
Class 12 · Mathematics
→If (A={1,2,3,4}), what is the ratio of the number of symmetric relations to the number of reflexive and symmetric relations?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R=A\times A-{(1,4),(4,1)}). Choose the correct classification.
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if both (a,b) are divisible by (2) or both (a,b) are divisible by (3). Choose the correct conclusion.
Class 12 · Mathematics
→On integers, (aRb) if and only if (a-b) is divisible by (4). What is the equivalence class of (3)?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a+b) is a prime number. Choose the correct classification.
Class 12 · Mathematics
→On non-zero real numbers, (aRb) if and only if (\frac{a}{b}) is rational. Choose the correct conclusion.
Class 12 · Mathematics
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