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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 a relation satisfies (R^{-1}\subseteq R), what is the correct conclusion about the symmetry of (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R) is symmetric and (R\subseteq S), which statement about (S) is correct?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf a symmetric relation on (A={1,2,3,4}) contains ((1,2),(2,1),(3,4),(4,3)) and no other off-diagonal pairs, how many off-diagonal pair groups are there?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R={(a,b):|a-b|<5}) is defined on real numbers, what is true about (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R={(a,b):\max(a,b)=\max(b,a)}) is defined on real numbers, what is true about (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf a symmetric relation on (A={1,2,3,4,5}) has exactly (3) off-diagonal pair groups and exactly (2) diagonal pairs, how many ordered pairs are there in total?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R=A\times A), which statement about (R) is correct?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R=\varnothing) is a relation on any set (A), what is true about (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R) is symmetric, what is true about (R^3=R\circ R\circ R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R) is symmetric and (R^2=R\circ R), which statement about (R^2) is correct?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R={(x,y):xy>0}) is defined on real numbers, which statement is correct about (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R) is symmetric on a set (A), what is true about (R\cap\Delta), where (\Delta={(a,a):a\in A})?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R) and (S) are symmetric, what is true about (R\triangle S), where (R\triangle S=(R-S)\cup(S-R))?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R) is symmetric on (A={1,2,3}) and contains exactly one diagonal pair and exactly two off-diagonal ordered pairs, how many such relations are possible?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R={(a,b):a\equiv b \pmod{3}}) is defined on integers, what is true about (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (A={1,2,3,4}) and (R) is symmetric with ((1,4)\notin R), which conclusion is definite?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf (R) is symmetric on (A={1,2,3,4}) and exactly one off-diagonal pair group is selected, how many off-diagonal ordered pairs are in (R)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf R is symmetric, which statement about A×A−R is correct?Class 12Relations and FunctionsSymmetric relationLevel 12Hard MathematicsIf (R) is a symmetric relation and (T) is a relation such that (R\subseteq T\subseteq R\cup R^{-1}), what is true about (T)?Class 12Relations and FunctionsSymmetric relationLevel 10Expert MathematicsIf a symmetric relation on (A={1,2,3}) has exactly (5) pairs, which value is possible for the number of diagonal pairs?Class 12Relations and FunctionsSymmetric relationLevel 10Expert