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Equivalence Classes

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) if and only if (a) and (b) have the same remainder when divided by (3). How many equivalence classes are formed?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsFor the relation on A={1,2,3,4,5,6} defined by “a and b are both multiples of 3 or both are not multiples of 3”, which statement is true?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn (A={1,2,3,4,5}), the classes of (R) are ({1,3,5}) and ({2,4}). How many pairs will be in (R)?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn (A={1,2,3,4}), the equivalence classes of (R) are ({1,2}) and ({3,4}). How many ordered pairs are in (R)?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn (A={1,2,3,4}), (R) is an equivalence relation with classes ({1,3}) and ({2,4}). How many ordered pairs are in (R)?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). What are the equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsLet R be an equivalence relation on A and let [a] and [b] denote equivalence classes. If aRb, which statement must be true?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if both (a) and (b) are multiples of (3), or both are not multiples of (3). What are the equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)}). What are its equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if both (a) and (b) are divisible by (2), or both are not divisible by (2). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsOn (A={1,2,3,4}), (R) is an equivalence relation. If (1R2) and (3) is not related to any other distinct element, which classes are possible?Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsOn (A={1,2,3,4}), (aRb) if and only if (a=b) or (a+b=5). What are the equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) have the same remainder when divided by (3). What are the equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) have the same parity. What are its equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 4Hard MathematicsWhich statement is correct about two equivalence classes formed by an equivalence relation?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsIf (A={1,2,3,4,5,6}) and (aRb) if (a) and (b) have the same remainder on division by (3), how many equivalence classes are formed?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsOn integers, (aRb) if (a-b) is divisible by (4). Which is the equivalence class of (1)?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsFor the same relation on (A={1,2,3,4}), what are the equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsFor (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), what are the equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 5Medium MathematicsIf (A={1,2,3,4}) and (R) is defined by having the same remainder when divided by (2), how many classes does (R) form?Class 12Relations and FunctionsTypes of relationsLevel 5Medium