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Transitivity

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

MathematicsFor R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,4),(4,2)} on A={1,2,3,4}, which missing ordered pair directly witnesses that R is not transitive?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsLet A={1,2,3,4,5} and define aRb if and only if a+b is odd. Which statement correctly describes this relation?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsIf R and S are transitive relations on the same set, which statement about their union R∪S is always valid?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsLet R be an equivalence relation on A and let [a] and [b] denote equivalence classes. If aRb, which statement must be true?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsOn (A={1,2,3,4}), (R) is an equivalence relation. If (1R2) and (2R4), which conclusion is necessary?Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). Which property fails?Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). Which failure prevents it from being an equivalence relation?Class 12Relations and FunctionsTypes of relationsLevel 4Hard MathematicsIf (R) is an equivalence relation and (aRb), (bRc), which conclusion is correct?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsIf (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,3)}), why is (R) not a partial order?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsWhy is (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}) on (A={1,2,3}) not an equivalence relation?Class 12Relations and FunctionsTypes of relationsLevel 5Medium MathematicsWhich relation is symmetric but not transitive?Class 12Relations and FunctionsTypes of relationsLevel 5Medium MathematicsWill the union of two transitive relations always be transitive?Class 12Relations and FunctionsTypes of relationsLevel 4Medium MathematicsIf a relation has all diagonal pairs and the reverse of every pair, which property remains to be checked to prove it is an equivalence relation?Class 12Relations and FunctionsTypes of relationsLevel 6Easy MathematicsWhy is (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) not an equivalence relation on (A={1,2,3})?Class 12Relations and FunctionsTypes of relationsLevel 6Easy MathematicsWhich pair must belong to the smallest equivalence relation on A={1,2,3,4} containing R={(1,2),(2,3),(4,4)}?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Expert MathematicsIs the union of two equivalence relations always an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Expert MathematicsIf (R) on (A={1,2,3}) is reflexive and symmetric and ((1,2)) and ((2,3)) are in (R), which pairs must be present to make it an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsWhich transitivity requirement fails for R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4)} on A={1,2,3,4}?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard 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 RelationsLevel 3Hard MathematicsWhat is the smallest change needed to make R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)} an equivalence relation on A={1,2,3}?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard