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Transitivity

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

MathematicsLet R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,4), (4,2)} be a relation on A = {1, 2, 3, 4}. Which of the following properties does R fail to satisfy?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsIf \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\), which single ordered pair must be added to make \(R\) transitive?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsIs the union of two transitive relations always transitive? Choose the correct option.Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsOn (A={1,2,3,4,6,12}), (aRb) means (a\mid b). Due to transitivity, which pair must follow from ((2,6)) and ((6,12))?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsOn the set (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) is given. Which property fails for (R)?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsLet \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)\}\) be a relation on \(A=\{1,2,3\}\). Why is \(R\) not an equivalence relation?Class 11Relations and FunctionsRelationsLevel 27Hard 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 MathematicsOn A = {1, 2, 3, 4, 5}, let R = {(1,2), (2,4), (4,5)}. What is the minimum number of pairs that must be added to make R transitive?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsFor (A={1,2,3}), the matrix of relation is (M_R=\begin{pmatrix}1&1&0\0&1&1\0&0&1\end{pmatrix}). Choose the correct statement.Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsA relation R on the set of real numbers is defined by aRb if and only if |a| = |b|. What type of relation is R?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn the set \(A=\{2,3,4,6,8,12\}\), relation \(R\) is defined by \(aRb\) if and only if \(a\mid b\). If \((2,6)\in R\) and \((6,12)\in R\), which of the following pairs must belong to \(R\) by transitivity?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b \text{ is odd}}). What is the correct option for this relation?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsFor R = {(a,b): |a − b| ≤ 1} on A = {1,2,3,4}, which statement is correct?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Hard MathematicsWhy is R = {(1,2), (2,3)} not transitive on A = {1,2,3}?Class 11Relations and FunctionsRelationsLevel 25Easy