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Transitivity Failure

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

MathematicsIf (A={1,2,3}), (R) has classes ({1,2},{3}), and (S) has classes ({1},{2,3}), why is (R\cup S) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all lines, (lRm) if and only if (l) and (m) intersect. Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn real numbers, (aRb) if and only if (|a-b|<1). Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}) is given. Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn integers, (aRb) holds when (a-b) is divisible by (8) or by (12). Why is this relation not an equivalence relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5}), (aRb) holds when (|a-b|\leq 1). Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn integers, (aRb) holds when (a-b) is divisible by (4) or by (6). Why is this relation not an equivalence relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3}), why is (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2)}). Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationEasy