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RELATED QUESTIONS

Equivalence Relation

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

MathematicsIf (R) is an equivalence relation, choose the correct statement about (R^{-1}).Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4}), (R={(a,b):a=b\text{ or }a+b\text{ is even}}). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if both (a,b) are odd or both are even. Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsHow many equivalence relations can be formed on (A={1,2,3})?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsIf (A={1,2,3,4,5}) and the sizes of equivalence classes are (2,2,1), how many ordered pairs are in the relation?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4}), (aRb) if and only if the difference between (a) and (b) is divisible by (2). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (a\equiv b \pmod{2}) and (a\equiv b \pmod{3}). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). How many ordered pairs are in the relation?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn non-zero real numbers, (aRb) if and only if (\frac{a}{b}) is rational. Choose the correct conclusion.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),(1,3),(3,1),(2,3),(3,2)}). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4,5,6}), the classes of (R) are ({1,2},{3,4,5},{6}). How many ordered pairs are in (R)?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsIf (R) is an equivalence relation and ([a]=[b]), which statement is correct?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if both (a) and (b) are odd or (a=b). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsIf (A={1,2,3,4}) and the partition for (R) is ({1,2,3},{4}), how many ordered pairs will be in (R)?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4}), (aRb) if and only if (a-b) is even. How many ordered pairs will the relation contain?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4}), (aRb) if and only if (a=b) or ({a,b}={1,3}). What type of relation is it?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn real numbers, (aRb) if and only if (a=b) or (a=-b). Choose the correct conclusion.Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsIf (R) and (S) are equivalence relations, which statement is correct for (R\cup S)?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsIf (R) and (S) are equivalence relations, which statement about (R\cap S) is correct?Class 12Relations and FunctionsTypes of relationsLevel 5Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,4),(4,1),(2,4),(4,2)}). Choose the correct statement.Class 12Relations and FunctionsTypes of relationsLevel 5Expert