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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।

MathematicsOn (A={1,2,3,4}), relation (R={(a,b):a\cdot b\text{ is even}}) is defined. Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) is a symmetric relation and it has (7) pairs in total, what is correct about the number of off-diagonal pairs?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsA relation (R) on a set (A) is symmetric. If ((x,y)\notin R), which statement is definitely true?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) is symmetric on (A) and (T\subseteq R), which statement about (T) is not always true?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsA relation on (A={1,2,3}) has matrix (M). If (M) is not a symmetric matrix, which conclusion is definitely correct?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn (A={1,2,3,4}), relation (R={(a,b):a-b\text{ is divisible by }2}) is given. Choose the correct option for (R).Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) is a symmetric relation, which statement about (R^{-1}) is correct?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsWhich of the following relations on (A={1,2,3}) is symmetric but not transitive?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) and (S) are two symmetric relations on (A), which statement is always true?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn the set of real numbers, relation (R) is defined by (aRb) if ((a-b)^2=0). What is correct about (R)?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn (A={1,2,3,4}), relation (R={(a,b):|a-b|=1}) is given. Choose the correct statement.Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf the matrix of a relation (R) is (M=\begin{pmatrix}1&0&1\0&1&0\1&0&0\end{pmatrix}), what can be said about (R)?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn (A={1,2,3}), how many symmetric relations contain all reflexive pairs?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsA set (A) has (n) elements. What is the total number of symmetric relations on (A)?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf a relation on (A={1,2,3}) is (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}), which minimum pair must be added to make (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsLet (A={1,2,3,4}) and (R={(a,b):a+b\text{ is even}}). Choose the correct statement about relation (R).Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsWhich statement gives the correct definition of a symmetric relation?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsWhen will the relation (R={(a,b):d(a,b)=2}) be symmetric, where (d) is a distance function?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a^2+b^2\text{ is even}}). Which statement is correct about (R)?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsIf (R) is a symmetric relation, what is (R\cup R^{-1}) equal to?Class 12Relations and FunctionsSymmetric relationLevel 11Hard