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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 (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both prime or both not prime. What is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsFor the relation (\lfloor a\rfloor=\lfloor b\rfloor) on real numbers, which is the equivalence class of (2.7)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsIn the previous relation on integers where two integers are related if both are positive or both are not positive, which is the equivalence class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsFor (A={1,2,3,4}), let (R=A\times A). How many equivalence classes does this relation have?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsIf (R) is an equivalence relation, why can ([a]) not be empty?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsIf (R) is an equivalence relation and ([a]=A), which statement about (a) is correct?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both less than (4) or both not less than (4). What is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsFor the relation on natural numbers based on having the same number of digits, which is the equivalence class of (145)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (a\equiv b \pmod{5}). Which is the equivalence class of (9)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsIn the relation on (A={1,2,3,4,5,6}) based on being multiples of (3) or not multiples of (3), what is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a+b) is divisible by (2). Which is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsFor the relation on real numbers where (a-b) is an integer, which element is in the same class as (\frac{1}{2})?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsOn (A={-2,-1,0,1,2}), (aRb) holds when (a^2=b^2). Which is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsOn (A={1,2,3,4,5,6,7}), (aRb) holds when (a) and (b) have the same remainder on division by (3). Which is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsOn integers, (aRb) holds when (a-b) is divisible by (7). Which is the equivalence class of (15)?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsOn integers, (aRb) is defined when (a-b) is divisible by (6). Which is the equivalence class of (20)?Class 12Relations and FunctionsEquivalence relationLevel 16MediumMathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) give the same remainder on division by (3). Which statement is correct?Class 12Relations and FunctionsEquivalence relationLevel 16MediumMathematicsIf (A) has (n) elements, how many equivalence classes are formed by the universal relation (A\times A)?Class 12Relations and FunctionsEquivalence relationLevel 16MediumMathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a\equiv b \pmod{4}). What is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 16MediumMathematicsFor the relation on real numbers where (a-b) is rational, which element is definitely in the same equivalence class as (\sqrt{2})?Class 12Relations and FunctionsEquivalence relationLevel 16Medium