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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 natural numbers, (aRb) when (a=b). What type of relation is (R)?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsWhich relation is generally not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsWhich relation is the best example of an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={0,1,2,3,4,5}), (aRb) when (a \equiv b \pmod{3}). Which is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={1,2,3,4}), (R) contains pairs whose two numbers have the same remainder on division by (2). What is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsWhich is the correct identification of the transitive property?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsWhich is the correct identification of the symmetric property?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsWhich property checks that for every (a\in A), ((a,a)\in R)?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn integers, (aRb) when (a+b) is even. Choose the correct conclusion.Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn integers, (aRb) when (a \equiv b \pmod{3}). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsIf (R) is an equivalence relation, what generally forms the equivalence class of (a)?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsHow does an equivalence relation organize a set?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsThe set (A={1,2,3,4}) is divided into parts ({1,3}) and ({2,4}). What type of relation is being in the same part?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={1,2,3}), (R={(1,1),(2,2)}). Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsIf (R) is an equivalence relation and ((a,b)\in R), ((b,c)\in R), what follows by the transitive property?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsIf (R) is an equivalence relation and ((a,b)\in R), then which pair must belong to (R) due to the symmetric property?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsFor a non-empty set (A), which statement is correct about the equality relation (R={(a,a):a\in A})?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn the set (A={1,2,3}), the universal relation (R=A\times A) is given. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={1,2,3,4}), (aRb) means (a) and (b) are both even or both odd. Choose the correct statement about (R).Class 12Relations and FunctionsEquivalence relationLevel 17Easy