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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।

MathematicsOn A = {1,2,3}, let R = {(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}. Which pair or pairs must be added to make R an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 26Hard MathematicsOn integers, (aRb) if (|a-b|\leq 2). Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsA relation (R) on a set (A) is reflexive and symmetric but not transitive. Which conclusion about (R) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsIf (R) and (S) are equivalence relations, which statement is generally true about (R\cup S)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn non-zero real numbers, (aRb) holds when (\frac{a}{b}\in\mathbb{Q}). If (aRb) and (bRc), which expression is useful to prove transitivity?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5}), relation (R) contains all diagonal pairs, ((1,2),(2,1),(2,5),(5,2)). Which minimum pairs must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsIf (R) is an equivalence relation and (a\in[b]), (b\in[c]), which conclusion is correct?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5}), relation (R) contains all diagonal pairs and ((1,2),(2,1),(2,4),(4,2)). Which minimum pairs must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3}), in (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}), which pair is necessary for transitivity?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn (A={1,2,3,4}), the relation (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}) is not an equivalence relation. Which missing pair shows the failure of transitivity?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsIf (R) is an equivalence relation and ((1,2)\in R), ((2,5)\in R), which pair must be present?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsOn (A={1,2,3,4}), (R={(1,2),(2,3),(3,1),(1,3),(2,1),(3,2),(1,1),(2,2)}). Which pair is missing for transitivity?Class 12Relations and FunctionsTransitive relationLevel 15Expert MathematicsOn (A={1,2,3,4}), (R={(1,2),(2,3),(3,2),(2,1),(1,3),(3,1)}). Which pair is missing for transitivity?Class 12Relations and FunctionsTransitive relationLevel 15Expert MathematicsOn a set, (R) and (S) are both transitive relations. Which statement is always true?Class 12Relations and FunctionsTransitive relationLevel 14Expert MathematicsA relation (R) on a set is transitive. If ((a,b) \in R), ((b,c) \in R), and ((c,d) \in R), which ordered pair must definitely be in (R)?Class 12Relations and FunctionsTransitive relationLevel 14Expert MathematicsOn (A={1,2,3,4,6,12}), (aRb) is defined when (a) divides (b). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationLevel 14Expert MathematicsOn (A={2,3,4,6,12}), (aRb) is defined when (a) divides (b). Which statement correctly proves transitivity?Class 12Relations and FunctionsTransitive relationLevel 13Expert MathematicsOn (A={1,2,3,4}), (R={(1,2),(2,3),(3,1),(1,3),(2,1)}). Which pair must be present for transitivity but is missing?Class 12Relations and FunctionsTransitive relationLevel 13Expert MathematicsOn (A={1,2,3,4}), the relation is (R={(a,b):a<b}). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationLevel 13Expert