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Equivalence Relation

Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (R={(x,y)\in \mathbb{R}\times\mathbb{R}:x^2=y^2}), which statement is correct for (R)?Class 11Relations and FunctionsRelationsLevel 26Expert MathematicsOn (A={1,2,3,4,5}), (R={(a,b):a-b\text{ is divisible by }2}). What type of relation is (R)?Class 11Relations and FunctionsRelationsLevel 26Expert MathematicsLet R be a relation on a set A defined by: for every a, b ∈ A, aRb if and only if a = b. What type of relation is R?Class 11Relations and FunctionsRelationsLevel 26Expert MathematicsA relation R is defined on the set A={1,2,3,4} by R={(a,b): a-b∈{0,2,-2}}. Which of the following statements is correct?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsOn the real numbers, define aRb if and only if a^3 = b^3. What type of relation is R?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn (A={1,2,3,4}), which statement is correct for (R={(a,b):a+b \text{ is even}})?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn the set A={1,2,3}, which pair must be added, at minimum, to make the relation R={(1,1),(2,2),(3,3),(1,2),(2,1)} an equivalence relation?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsFor the relation \(R=\{(a,b):a\ne b\}\) on the set \(A=\{1,2,3\}\), choose the correct statement.Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsWhich properties are required for a relation R on a set A to be an equivalence relation?Class 11Relations and FunctionsRelationsLevel 25Medium MathematicsOn the set \(A=\{1,2,3,4\}\), let \(R=\{(a,b)\in A\times A:a-b>0\}\). Which statement about this relation is correct?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsWhat is R = {(a,b): a² = b²} on A = {-2,-1,1,2}?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Hard MathematicsOn the set of real numbers \(\mathbb R\), a relation \(R\) is defined by \(xRy\iff x-y\in\mathbb Q\). Choose the correct classification of this relation.Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn A = Z, define aRb when a − b is divisible by 3. What type of relation is this?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsIf (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2)}), why is (R) not an equivalence relation?Class 11Relations and FunctionsRelationsLevel 26Medium MathematicsOn (A={1,2,3}), is (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) an equivalence relation?Class 11Relations and FunctionsRelationsLevel 26Medium MathematicsLet \(S=\{1,2,3\}\). Which of the following relations on \(S\) is an equivalence relation?Class 11Relations and FunctionsRelationsLevel 26Medium MathematicsIf (R) is an equivalence relation, which three properties must it have?Class 11Relations and FunctionsRelationsLevel 25Medium MathematicsFor R = {(1,1), (2,2), (3,3)} on A = {1,2,3}, which statement is correct?Class 11Relations and FunctionsRelationsLevel 25Easy MathematicsOn (A={1,2,3,4,5}), if (aRb) when (a-b) is even, what type of relation is (R)?Class 11Relations and FunctionsRelationsLevel 25Medium