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Equivalence Class

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

MathematicsOn the set of real numbers, (aRb) if and only if (\lfloor a\rfloor=\lfloor b\rfloor). Which is the equivalence class of (2.4)?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a) and (b) leave the same remainder when divided by (4). Which elements are in the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same unit digit. Which statement about this relation is correct?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}). Which partition is obtained from this relation?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn real numbers, (aRb) if and only if (a-b) is rational. Choose the correct statement about the equivalence classes of this relation.Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn (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 relationLevel 16ExpertMathematicsOn the set (A={1,2,3,4,5,6}), (aRb) if and only if (\gcd(a,6)=\gcd(b,6)). How many elements are in the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn the set of real numbers, (aRb) if and only if (|a|=|b|). What is the equivalence class of (-3) for this relation?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn the set of integers (Z), (aRb) if and only if (a-b) is divisible by (5). Which is the equivalence class of (7)?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn (A={1,2,3,4}), for (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}), what is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn real numbers, (aRb) holds when (a-b) is rational. Which statement is correct?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn integers, (aRb) holds when (a-b) is divisible by (7). What is ([3]\cap[10])?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsFor points in the plane, ((x_1,y_1)R(x_2,y_2)) holds when (x_1+y_1=x_2+y_2). Which is the equivalence class of ((2,-1))?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (a) and (b) have the same greatest common divisor with (9). Which is the equivalence class of (6)?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when the digit sums of (a) and (b) give the same remainder modulo (3). Which is the equivalence class of (8)?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn real numbers, (aRb) holds when (|a-1|=|b-1|). Which is the equivalence class of (-2)?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a) and (b) have the same status of divisibility by (3) and by (4). Which is the equivalence class of (8)?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn (A={1,2,3,4,5,6,7,8,9,10}), (aRb) holds when (\tau(a)=\tau(b)), where (\tau(n)) is the number of positive divisors. Which is the equivalence class of (6)?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn real numbers, (aRb) holds when (\cos a=\cos b). Which is the correct form of the equivalence class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn integers, (aRb) holds when (a\equiv b \pmod{4}), and (aSb) holds when (a\equiv b \pmod{6}). In (R\cap S), what is the equivalence class of (14)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard