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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 MathematicsIf (R) and (S) are equivalence relations on a set (A), how can the equivalence classes of (R\cap S) be understood?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all real numbers, (aRb) if and only if (\cos^2 a=\cos^2 b). Which of the following must be in the equivalence class of (\frac{\pi}{3})?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all real numbers, (aRb) if and only if (a^2-a=b^2-b). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsIf (R) and (S) are equivalence relations on the same set (A), which statement about (R\cap S) is correct?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all positive real numbers, (aRb) if and only if (\log a-\log b\in Z). Which is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all non-zero real numbers, (aRb) if and only if (\frac{a}{b}\in Q). What type of relation is this?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn real numbers, (aRb) if and only if (a-b\in Z). Which is the correct form of the equivalence class of (1.7)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same set of prime factors. Which of the following belongs to the equivalence class of (12)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4}), (aRb) if and only if (a^2-b^2) is divisible by (3). What is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsIf (R) is transitive and contains ((a,b)), ((b,c)), and ((c,a)), which statement is correct?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R) is transitive and contains ((1,2),(2,3),(3,1)), toward what does the whole ({1,2,3}) part move?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R) is transitive, what can be said about (R\circ R\subseteq R)?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R) and (S) are symmetric relations, which statement about the composition (R\circ S) is always true?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) and (S) are both reflexive on (A), which middle element works to show (S\circ R) is reflexive?Class 12Relations and FunctionsReflexive relationHard