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Equivalence Relation

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

MathematicsOn real numbers, (aRb) if and only if (a-b\in Z). Choose the correct classification.Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4,6,12}), (aRb) if and only if (a) divides (b) and (b) divides (a). Choose the correct statement.Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4)}). Choose the correct classification.Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsFor a non-empty set (A), which statement is correct for the universal relation (A\times A)?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn (A={1,2,3,4}), (R) is an equivalence relation. If (1R2) and (2R4), which statement is necessary?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsIf (R) is an equivalence relation on a set and (aRb), which statement is necessary?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsIf (R) is an equivalence relation and (aRb), (bRc), (cRd), which conclusion is necessary?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn real numbers, (aRb) if and only if (a^3=b^3). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsFor the relation defined by aRb iff a=b or both a and b are greater than 2 on A={1,2,3,4}, what is the equivalence class of 3?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1),(2,4),(4,2)}). What type of relation is it?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsFor R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,4),(4,2)} on A={1,2,3,4}, which missing ordered pair directly witnesses that R is not transitive?Class 12Relations and FunctionsTypes of relationsLevel 4Expert 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 MathematicsLet A={1,2,3,4,5} and define aRb if and only if a+b is odd. Which statement correctly describes this relation?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}), (aRb) if and only if (a=b) or (a+b=5). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn real numbers, (aRb) if and only if (a-b) is rational. Choose the correct classification.Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn real numbers, (aRb) if and only if (a^2=b^2). What type of relation is it?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn integers, (aRb) if and only if (a-b) is divisible by (7). Choose the correct conclusion.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}), (aRb) if and only if (a=b) or (a+b=5). What is the correct conclusion?Class 12Relations and FunctionsTypes of relationsLevel 6Hard