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Symmetric Relation

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (R) is a symmetric relation on a set (A), which statement is true for (R^{-1})?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsOn (A={1,2,3,4}), the matrix of a relation is (\begin{pmatrix}1&0&1&0\0&1&0&1\1&0&0&0\0&1&0&1\end{pmatrix}). What type is the relation?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsIf (A) has (n) elements, which is the total number of symmetric relations on (A)?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsFor a set (A) with four elements, how many symmetric relations contain all diagonal pairs necessarily?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsOn (A={a,b,c}), a symmetric relation contains ((a,b)) and ((c,a)). Which pairs must be present at minimum?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsOn (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2),(1,1)}). Is (R) symmetric or not?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a-b\text{ is divisible by }2}). Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsOn the set (A={1,2,3,4,5}), the relation (R={(a,b):a+b\text{ is even}}) is given. Is (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}). What is the minimum number of pairs to remove to make the relation symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a\equiv -b \pmod{5}}). What is the correct statement about (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsWhich statement gives the most accurate definition of a symmetric relation?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsWhich relation on (\mathbb{R}) is symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(1,2),(2,1),(3,4)}). What must be done to make (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsIf (M) is the matrix of a relation (R), what is the correct matrix condition for (R) to be symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), how many symmetric relations contain ((1,2)) but not ((2,1))?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), how many symmetric relations must contain both ((1,2)) and ((3,4))?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsIf (A) has (6) elements, how many symmetric relations are there on (A)?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a^2+b^2=10}). What type of relation is (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a+2b=6}). Is (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a-b\text{ is odd}}). What is (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Hard