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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}), what equivalence classes are formed by (R={(1,1),(2,2),(3,3),(1,2),(2,1)})?Class 12Relations and FunctionsTypes of relationsLevel 6Easy MathematicsWhat does an equivalence relation form in a set?Class 12Relations and FunctionsTypes of relationsLevel 5Easy MathematicsOn (A={1,2,3,4,5}), how many equivalence relations have exactly two equivalence classes?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Expert MathematicsOn (A={1,2,3,4,5}), (aRb) iff (a\equiv b\pmod 3). How many equivalence classes are formed?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Expert MathematicsOn (A={1,2,3,4,5,6}), (aRb) iff (a) and (b) leave the same remainder on division by (2). How many equivalence classes are formed?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Expert MathematicsOn (A={1,2,3,4,5}), how many equivalence relations have exactly three equivalence classes?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Expert MathematicsOn (A={1,2,3,4}), how many equivalence relations have exactly two equivalence classes?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Expert MathematicsHow many ordered pairs does the equivalence relation with classes {1,2} and {3,4} contain?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsIf the classes of (R) on (A={1,2,3,4}) are ({1,2}) and ({3,4}), which pair must be in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsFor the relation on A={1,2,3,4} whose equivalence classes are {1,2} and {3,4}, which pair is definitely absent?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsIf all equivalence classes of (R) on (A={1,2,3,4}) are singletons, how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsIf equivalence classes of (R) on (A={1,2,3,4}) are ({1,4}), ({2}), and ({3}), how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsFor the partition ({{1},{2,3},{4,5}}) of (A={1,2,3,4,5}), how many pairs are in the equivalence relation formed by it?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsIf all equivalence classes of (R) on (A={1,2,3,4}) are singletons, what relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard MathematicsIf a relation (R) on (A={1,2,3,4}) forms two classes ({1,3}) and ({2,4}), how many pairs will be in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard MathematicsIf the classes of (R) on (A={1,2,3,4}) are ({1,2}) and ({3,4}), which pair will not be in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard MathematicsIf (R={(1,1),(2,2),(1,2),(2,1),(3,3)}) on (A={1,2,3}), what are the equivalence classes formed by (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard MathematicsFor the partition ({{1,4},{2,3}}) of (A={1,2,3,4}), how many pairs are in the equivalence relation formed by it?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). What are the equivalence classes?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsIf (R) is an equivalence relation and (aRb), what is true about ([a]) and ([b])?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard