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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 symmetric, which statement about R⁻¹ is correct?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (A={1,2,3,4,5}), the number of symmetric relations on (A) equals which of the following?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf the matrix of a relation on (A={1,2,3}) is (M=\begin{bmatrix}1&1&0\0&1&1\0&1&1\end{bmatrix}), is the relation symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (A={1,2,3,4}) and (R={(a,b):a) and (b) have the same remainder when divided by (2)(}), choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn integers, the relation (R={(a,b):a-b=3}) is given. Why is it not symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsFor the relation (R={(a,b):a^2=b^2}) on the set of real numbers, what is the correct statement?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}), (R) is not symmetric because which pair is missing?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) and (S) are two symmetric relations on (A), choose the correct statement about (R\cup S).Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) and (S) are two symmetric relations on (A), what is true about (R\cap S)?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsFor the relation (R={(x,y):x-y\text{ is odd}}), where (x,y\in {1,2,3,4}), which statement is correct?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (A={1,2,3,4}) and (R={(a,b):a\le b}), why is (R) not symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (A={1,2,3}) and (R={(a,b):a+b\text{ is even}}), choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (A={1,2,3,4}) and (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1),(2,4)}), which ordered pair must be added at minimum to make (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,1),(2,3),(3,2)}), which property does (R) definitely have?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn (A={1,2,3,4}), how many symmetric relations must contain ((1,2)) and must not contain ((3,4))?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsWhich statement is true for a symmetric relation but generally not true for an antisymmetric relation?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf a relation (R) contains ((1,2),(2,1),(2,3),(3,2),(1,3)) and no other off-diagonal pair, what is necessary for symmetry?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn (A={1,2,3,4}), relation (R={(a,b):a+b=5}) is defined. Is (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsOn (A={1,2,3}), how many symmetric relations contain exactly one diagonal pair?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) is symmetric, then (R\cap R^{-1}) is equal to which of the following?Class 12Relations and FunctionsSymmetric relationLevel 12Hard