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Symmetric Relation

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

MathematicsFor A = {1,2,3,4}, let R = {(a,b) : a+b=5}. What is the correct statement about R?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 27Medium MathematicsIf \((2,5)\in R\) and the relation \(R\) is symmetric, which of the following pairs must also belong to \(R\)?Class 11Relations and FunctionsRelationsLevel 26Expert MathematicsIf A={1,2,3,4} and R={(a,b)∈A×A : ab is even}, which statement about R is correct?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsFor which type of relation is the inverse relation equal to the relation itself, that is, \(R^{-1}=R\)?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsOn the set of real numbers, a relation R is defined by aRb if and only if \(|a-b|\leq 2\). Choose the correct statement.Class 11Relations and FunctionsRelationsLevel 27Hard 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 MathematicsOn the set \(A=\{1,2,3,4,5\}\), let \(R=\{(a,b)\in A\times A:a+b\le 6\}\). Choose the correct statement.Class 11Relations and FunctionsRelationsLevel 25Hard 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 MathematicsIf \(R\) is a symmetric relation and \((2,5)\in R\), which of the following pairs must definitely belong to \(R\)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn the set \(A=\{1,2,3,4,5,6\}\), consider the relation \(R=\{(a,b):\gcd(a,b)=1\}\). Which of the following properties is true for this relation?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsFor the relation \(R=\{(a,b):|a-b|=2\}\) defined on the set \(A=\{1,2,3,4,5\}\), which of the following properties is true?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsFor the relation R = {(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)} on the set A = {1, 2, 3}, choose the correct statement.Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsSet A has 3 elements. How many symmetric relations are there on A?Class 11Relations and FunctionsCounting symmetric relationsLevel 25Hard MathematicsIf A = {1, 2, 3, 4, 5} and R = {(a, b) ∈ A × A : a + b = 6}, then what type of relation is R?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsIf R = {(a,b): a ≠ b} on A = {1,2,3}, is R symmetric?Class 11Relations and FunctionsRelationsLevel 25Medium MathematicsIf A = {1, 2, 3, 4} and R = {(x, y) : x + y = 5}, which property does R have?Class 11Relations and FunctionsRelationsLevel 26Medium MathematicsWhen is a relation R called symmetric?Class 11Relations and FunctionsRelationsLevel 26Easy MathematicsLet \(S=\{1,2,3\}\). Which of the following relations on \(S\) is an equivalence relation?Class 11Relations and FunctionsRelationsLevel 26Medium MathematicsIf R = {(1, 2), (2, 1), (3, 3)}, what is the main reason that R is symmetric?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 26Medium MathematicsIf the relation \(R\) is symmetric and \((5,8)\in R\), which of the following statements must be true?Class 11Relations and FunctionsRelationsLevel 25Medium