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Partition

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\equiv b \pmod{3}). What are the distinct equivalence classes of this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsAn equivalence relation on a set (A) has equivalence classes ({a,b,c}), ({d,e}), and ({f}). How many ordered pairs are there in this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set (A={1,2,3,4,5}), (aRb) if and only if (a) and (b) are both even or both odd. How many blocks are formed in the partition by this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsHow many equivalence relations on (A={1,2,3,4,5}) have (1) alone in its own class?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsIf (R) is an equivalence relation and ([a]\cap[b]\cap[c]\neq\varnothing), which statement is correct?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsHow many equivalence relations on (A={1,2,3,4}) have (1) and (2) in different classes?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsHow many equivalence relations on (A={1,2,3,4,5}) have (1,2,3) in the same class?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5}), the classes of relation (R) are ({1,4,5}) and ({2,3}). Which pair will definitely not be in (R)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5}), (aRb) holds when (a) and (b) are both greater than (2) or both not greater than (2). Which partition is formed by this relation?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsIf (R) is an equivalence relation, when will ([a]\cup[b]) be a single equivalence class?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsFor the same partition ({1,6},{2,5},{3,4}), which pair will not belong to the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsFor the partition ({1,6},{2,5},{3,4}) of (A={1,2,3,4,5,6}), which pair belongs to the corresponding equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsWhich statement correctly describes the connection between an equivalence relation and a partition?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsIf (R) is an equivalence relation and ([a]\neq[b]), which statement is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsIf an equivalence relation partitions a set into ({2,4,6},{1,3},{5}), which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{2}). Which partition is formed by this relation?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf (R) is an equivalence relation on a set (A), what does ({[a]:a\in A}) represent?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsWhich option gives a valid partition of (A={1,2,3,4,5})?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf an equivalence relation has classes ({p,q,r}) and ({s}), how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsAn equivalence relation on (A={a,b,c,d}) has classes ({a,c}) and ({b,d}). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Medium