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Inverse Relation

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

MathematicsIn which case will the inverse relation of (f:A\to B) become a function from (f(A)) to (A)?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf a function (f:A\to B) is one-one, what is the correct statement about its inverse relation?Class 12Relations and FunctionsOne-one functionHard MathematicsIf (f:A\to B) is a function and (f^{-1}) is also a function, which statement about (f) is definitely true?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2), why is (f^{-1}) not a function?Class 12Relations and FunctionsFunctionsHard MathematicsOn a set (A), (R) is a transitive relation. Which statement about (R^{-1}) is always true?Class 12Relations and FunctionsTransitive relationHard MathematicsOn real numbers, (aRb) if (a-b\in\mathbb{Q}). What type will (R^{-1}) be?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}), what type will (R^{-1}) be?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R) is transitive, which statement is correct about (R^{-1})?Class 12Relations and FunctionsTransitive relationHard MathematicsA relation (R) on a set (A) is symmetric. Choose the correct statement about (R^{-1}).Class 12Relations and FunctionsSymmetric relationExpert MathematicsFor any relation R, which statement about R ∪ R⁻¹ is always true?Class 12Relations and FunctionsSymmetric relationMedium MathematicsIf (R) is symmetric and (T=R\cup R^{-1}), which statement about (T) is correct?Class 12Relations and FunctionsSymmetric relationExpert MathematicsA relation (R) on a set (A) is symmetric. Which statement about (R^{-1}) is correct?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) is symmetric, what is true about (R^3=R\circ R\circ R)?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) is a symmetric relation and (T) is a relation such that (R\subseteq T\subseteq R\cup R^{-1}), what is true about (T)?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R\cap R^{-1}=R), what is the correct conclusion about (R)?Class 12Relations and FunctionsSymmetric relationExpert MathematicsFor a relation (R), what is the smallest symmetric relation that contains (R)?Class 12Relations and FunctionsSymmetric relationExpert MathematicsFor any relation R, which statement about R ∪ R⁻¹ is always true?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) is a symmetric relation, what is true about (R\cup R^{-1})?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) and (S) are symmetric relations, which additional condition is sufficient for (R\circ S) to be symmetric?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf a relation (R) satisfies (R=R^{-1}), what is the correct conclusion about (R)?Class 12Relations and FunctionsSymmetric relationHard