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Equivalence

Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsWhich statement is equivalent to \(-1<x\le 6\) ?Class 11Linear InequalitiesIntroduction to inequalitiesExpert MathematicsIf (R) and (S) are both equivalence relations on (A), which statement about (R\cap S) is always true?Class 11Relations and FunctionsRelationsExpert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) have the same greatest prime factor. What kind of relation is it?Class 11Relations and FunctionsRelationsExpert MathematicsOn (A={1,2,3,4}), (R={(a,b):a-b) is divisible by (3)(}). How many ordered pairs are in (R)?Class 11Relations and FunctionsRelationsExpert MathematicsOn (A={1,2,3}), the identity relation is (I_A={(1,1),(2,2),(3,3)}). What is the correct nature of (I_A)?Class 11Relations and FunctionsRelationsExpert MathematicsRelation (R) is defined on (A={1,2,3}) by (R=A\times A). Which statement about (R) is correct?Class 11Relations and FunctionsRelationsExpert MathematicsOn (\mathbb{R}), (aRb) if and only if (a^2=b^2). Which statement about (R) is correct?Class 11Relations and FunctionsRelationsExpert MathematicsFor (A={1,2,3,4}), relation (R={(a,b):a\equiv b\pmod{2}}). Which partition is formed by (R)?Class 11Relations and FunctionsRelationsExpert MathematicsOn (\mathbb{Z}), (aRb) if and only if (a-b) is divisible by (4). How many equivalence classes are formed by this relation?Class 11Relations and FunctionsRelationsExpert MathematicsOn the set of real numbers (\mathbb{R}), (aRb) if and only if (a-b\in\mathbb{Z}). What is the nature of (R)?Class 11Relations and FunctionsRelationsExpert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (a+b) is even. What is the nature of (R)?Class 11Relations and FunctionsRelationsExpert MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), which statement is correct about (R)?Class 11Relations and FunctionsRelationsExpert MathematicsWhich option gives a partition of (A={1,2,3})?Class 11Relations and FunctionsRelationsExpert MathematicsIf (A={1,2,3,4}) and (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}), which statement about (R) is correct?Class 11Relations and FunctionsRelationsExpert MathematicsFor the universal relation (A\times A) on (A={1,2,3}), which statement is correct?Class 11Relations and FunctionsRelationsExpert MathematicsOn the set of integers, (aRb) means (a-b) is even. What type of relation is it?Class 11Relations and FunctionsRelationsExpert MathematicsIf (A={1,2,3,4}) and (R={(a,b):a-b \text{ is divisible by }2}), which statement about (R) is correct?Class 11Relations and FunctionsRelationsExpert MathematicsOn (A=\mathbb{R}\setminus{0}), (aRb) if and only if (ab>0). What are its equivalence classes?Class 11Relations and FunctionsRelationsHard MathematicsOn non-zero integers, (aRb) if and only if (\frac{a}{b}>0). What type of relation is it?Class 11Relations and FunctionsRelationsHard MathematicsOn positive integers, (aRb) if and only if (a\mid b) and (b\mid a). Which relation is this?Class 11Relations and FunctionsRelationsHard