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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={(1,1),(2,2),(1,2),(2,1),(3,3)}) on (A={1,2,3}), what are the equivalence classes formed by (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3,4}), if (aRb) when (a+b=5), why is (R) not transitive?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3,4}), if (aRb) when (a+b=5), which statement about (R) is correct?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3,4}), if (aRb) when (|a-b|) is divisible by (2), what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3}), relation (R) is defined by (aRb) if (|a-b|\le1). Which property is absent?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 is the correct statement about (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,3)}) on (A={1,2,3}), why is (R) not a partial order relation?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf a relation is both symmetric and antisymmetric, what is correct for distinct elements (a\ne b)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(1,3)}) on (A={1,2,3}), is (R) antisymmetric?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (A) is non-empty and (R=\varnothing), which statement is false?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R=A\times A) on (A={1,2,3}), which statement about (R) is false?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,4),(3,4)}), which pair must be in (R^{-1})?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,3),(3,1)}), which pair will be in (R^{-1}\circ R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R) is a relation and (R^{-1}=R), which conclusion is definite?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not a partial order relation?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf divisibility relation is defined on (A={1,2,4,8}), what type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIn the divisibility relation on ({2,3,6}), which is the least element?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIn the divisibility relation on ({1,2,3,6}), what are the least and greatest elements respectively?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsOn (A={1,2,3,4}), if (aRb) when (a) divides (b), which pair will not be in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard