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Relation Properties

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

MathematicsOn the set \(A=\{1,2,3\}\), let \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\). What is the equivalence class \([1]_R\) of \(1\) with respect to \(R\)?Class 11Relations and FunctionsRelationsLevel 26Expert MathematicsOn A = {1,2,3,4,5,6}, let R = {(a,b) : gcd(a,b) = 1}. Which property is correct for this relation?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 26Hard MathematicsFor which type of relation is the inverse relation equal to the relation itself, that is, \(R^{-1}=R\)?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsFor the empty relation ∅ on A = {1,2,3}, which statement is correct?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn A = {1,2,3,4}, let R = {(a,b) : a divides b}. Which statement about R is correct?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Hard MathematicsWhich properties are required for a relation R on a set A to be an equivalence relation?Class 11Relations and FunctionsRelationsLevel 25Medium MathematicsOn A = {1,2,3}, relation R = {(1,1),(2,2),(3,3),(1,2)} satisfies which property?Class 11Relations and FunctionsRelationsLevel 25Medium MathematicsWhy is the relation \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\) defined on the set \(A=\{1,2,3\}\) not transitive?Class 11Relations and FunctionsRelationsLevel 25Medium MathematicsOn A={1,2,3}, which type is the relation R={(1,1),(2,2),(3,3),(1,2)}?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Medium