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Introduction To Relations

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (R={(1,2),(2,1),(2,3)}), which pair must be in (R\circ R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,3)}) and (S={(2,4),(3,5)}), what is (S\circ R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,4),(4,1)}), what is (R^{-1})?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R) is symmetric and ((3,5)\in R), which statement about (R^{-1}) is correct?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}) on (A={1,2,3}), which property definitely fails?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,4),(1,4)}) on (A={1,2,3,4}), what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf divisibility relation is defined on (A={2,3,5,30}), which is the least element?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf divisibility relation is defined on (A={2,4,6,12}), which is the least element?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf divisibility relation is defined on (A={2,3,4,6,12}), which is the greatest element?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3,6}), if (aRb) when (a) divides (b), how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3,4,5}), if (aRb) when (a+b) is odd, how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3,4,5}), if (aRb) when (a+b) is even, how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (aRb) on (A={1,2,3,4,5,6,7,8}) when (a\equiv b \pmod{4}), what is the equivalence class of (1)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (aRb) on (A={1,2,3,4,5,6,7,8}) when (a-b) is divisible by (3), what is the equivalence class of (2)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (aRb) on (A={1,2,3,4,5,6}) when (a\equiv b \pmod{2}), how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsFor the partition ({{1},{2,3},{4,5}}) of (A={1,2,3,4,5}), how many pairs are in the equivalence relation formed by it?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsFor the partition ({{1,2},{3,4,5}}) of (A={1,2,3,4,5}), how many pairs are in the equivalence relation formed by it?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,3),(3,4),(1,3),(2,4)}), which minimum pair must be added to make it transitive?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (A={1,2,3,4}) and (R={(1,2),(2,3),(3,4)}), how many pairs will be in the transitive closure of (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (A) has (4) elements, how many relations on (A) are both symmetric and antisymmetric?Class 12Relations and FunctionsIntroduction to RelationsHard