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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}), the matrix of relation (R) is (\begin{pmatrix}1&1&0\0&1&1\0&1&1\end{pmatrix}). Which minimum entry must be changed for symmetry?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsIf (R) is a symmetric relation on (A), what is the correct statement about (R^{-1})?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsIf (R) and (S) are both symmetric relations on (A), which of the following relations is definitely symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a-b\text{ is positive}}). Why is (R) not symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}) is given. Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsA set (A) has (5) elements. If every symmetric relation (R) must contain all diagonal pairs, how many such relations are possible?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsHow many different symmetric relations can be formed on the set (A={1,2,3,4})?Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b=2b}). Choose the correct option about (R).Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b=2a}). Which statement is correct for (R)?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsIf a relation (R) contains only diagonal pairs of the form ((a,a)), which statement about (R) is correct?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsA relation on (A={1,2,3}) has the matrix (\begin{bmatrix}1&1&0\0&1&1\0&1&1\end{bmatrix}). Choose the correct statement.Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsA relation on (A={1,2,3}) has the matrix (\begin{bmatrix}1&0&1\0&1&0\1&0&0\end{bmatrix}). Is the relation symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b=7}). If ((3,4)\in R), which pair also belongs to (R) due to symmetry?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsIn which option are a relation (R) and its inverse (R^{-1}) equal?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsIf (R={(a,b):a+b\text{ is a multiple of }5}), which statement is correct based on symmetry?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsOn (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2),(1,3)}). Which pair should be added to make (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsOn (A={1,2,3,4,5}), (R={(a,b):\text{the difference of }a\text{ and }b\text{ is divisible by }2}). Is (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsOn (A={1,2,3,4}), (R={(a,b):a^2-b^2=0}). Which option is correct about (R)?Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b=ab}). Choose the correct statement for (R).Class 12Relations and FunctionsSymmetric relationLevel 12Medium MathematicsOn (A={1,2,3,4}), (R={(a,b):ab\text{ is even}}). Which statement is correct about (R)?Class 12Relations and FunctionsSymmetric relationLevel 12Medium