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Modular Arithmetic

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

MathematicsIf A = {1, 2, 3}, B = {0, 1}, and R = {(x, y): y ≡ x (mod 2)}, what is correct about R?Class 11Relations and FunctionsFunctions as a special kind of relationMedium MathematicsOn the set \(A=\{1,2,3,4,5,6\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\equiv b\pmod{3}\). What is the equivalence class \([2]\)?Class 11Relations and FunctionsRelationsExpert MathematicsOn the set \(A=\{1,2,3,4,5,6\}\), let \(R=\{(a,b):a-b\equiv 0\pmod{5}\}\). What is the equivalence class \([1]\) under this relation?Class 11Relations and FunctionsRelationsExpert MathematicsIf A = {1, 2, 3, 4, 5} and R = {(a, b) : a ≡ b (mod 4)}, what is the equivalence class [1] of 1 under R?Class 11Relations and FunctionsRelationsExpert MathematicsOn the set \(A=\{1,2,3,4,5,6\}\), relation \(R\) is defined by: \(aRb\) means that \(a\) and \(b\) leave the same remainder when divided by 2. What is the equivalence class \([2]\) of 2 under this relation?Class 11Relations and FunctionsRelationsExpert MathematicsOn the set \(A=\{1,2,3,\ldots,15\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\equiv b\pmod{6}\). Which of the following is the equivalence class \([8]\) in \(A\)?Class 11Relations and FunctionsRelationsHard MathematicsOn the set \(A=\{0,1,2,3,4,5,6,7\}\), define a relation \(R\) by \(aRb\) if and only if \(a^2\equiv b^2\pmod{8}\). What is the equivalence class \([1]_R\) of 1 under \(R\)?Class 11Relations and FunctionsRelationsHard MathematicsOn A = {0, 1, 2, 3, 4}, let R = {(a, b) : a + b ≡ 0 (mod 5)}. How many ordered pairs are in R?Class 11Relations and FunctionsRelationsMedium MathematicsOn the set \(A=\{0,1,2,3,4,5,6,7,8\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\equiv b\pmod{3}\). Which of the following is the equivalence class \([7]\)?Class 11Relations and FunctionsRelationsHard MathematicsOn A = {0, 1, 2, 3, 4, 5, 6, 7}, define aRb if and only if a − b is divisible by 4. How many equivalence classes are there?Class 11Relations and FunctionsRelations that are reflexive and symmetricMedium MathematicsOn the set \(A=\{1,2,3,4,5,6\}\), define a relation \(R\) by \(aRb\) if and only if \(a\equiv b\pmod{2}\). How many equivalence classes does this relation have?Class 11Relations and FunctionsRelationsHard MathematicsOn A = Z, define aRb when a − b is divisible by 3. What type of relation is this?Class 11Relations and FunctionsRelationsHard MathematicsIf the relation \(R\) on the set \(A=\{1,2,3,4,5,6\}\) is defined by \(aRb\) if and only if \(a\equiv b\pmod{3}\), what is the equivalence class of \(1\)?Class 11Relations and FunctionsRelationsMedium MathematicsIf A={1,2,3,4,5,6} and aRb when a≡b (mod 3), what is the equivalence class of 1?Class 11Relations and FunctionsRelations that are reflexive and symmetricMedium MathematicsIf \(A=\{0,1,2,3,4\}\), \(B=\{0,1,2,3,4\}\), and \(R=\{(a,b)\in A\times B: a^2\equiv b\pmod{5}\}\), what is the value of \(|R|\)?Class 11Relations and FunctionsRelationsExpert MathematicsIf (A={1,2,3,4}) and (B={0,1,2,3,4,5}), how many pairs ((a,b)) in (A\times B) satisfy (b\equiv a^2\pmod{5})?Class 11Relations and FunctionsCartesian product of setsExpert