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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 integers, (aRb) holds when (a-b) is a multiple of (5). How many distinct equivalence classes are there?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsOn (A={1,2,3,4}), for (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}), what are the equivalence classes?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsIf (R) is an equivalence relation on (A) and (aRb), what is true about the equivalence classes of (a) and (b)?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{3}). How many equivalence classes are formed?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsOn (A={1,2,3,4}), (aRb) holds when (a) and (b) are both even or both odd. What are the equivalence classes?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsIf two equivalence classes have even one common element, what is correct about them?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsWhat is correct about classes formed by an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsIf (R) is an equivalence relation, which statement about two equivalence classes is correct?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={1,2,3,4,5,6}), (aRb) when (a) and (b) leave the same remainder on division by (3). How many equivalence classes does (R) form?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={1,2,3,4}), what type of relation is (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1),(2,4),(4,2)})?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsAn equivalence relation divides a set into what?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsFor A={0,1,2,3,4,5} and R={(a,b): a²≡b² (mod 6)}, how many equivalence classes does R have?Class 12Relations and FunctionsReflexive relationLevel 7Hard MathematicsIf (R) is an equivalence relation on a set and (aRb) is false, what is true about ([a]) and ([b])?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsIf (R) is an equivalence relation and ([a]\cap[b]\neq\varnothing), which statement is correct?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsWhich relation on (A={1,2,3,4}) can have exactly two equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if both (a,b) are less than (4) or (a=b). Choose the correct equivalence classes.Class 12Relations and FunctionsTypes of relationsLevel 6Expert 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)}). How many equivalence classes does (R) have?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4}), (aRb) if and only if (a=b) or both (a) and (b) are less than (3). What are the correct equivalence classes?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsIf (R) is an equivalence relation and (a) and (b) lie in different equivalence classes, what is true about (aRb)?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). Choose the correct equivalence classes.Class 12Relations and FunctionsTypes of relationsLevel 5Expert