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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}), (R={(a,b):a-b\text{ is even}}). Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn (A={1,2,3,4}), (R={(a,b):|a-b|\text{ is even}}). What is (R)?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsIf (R) and (S) are symmetric, is (R-S) always symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsIf (R) is symmetric, which statement about (A\times A-R) is correct?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn (A={1,2,3,4}), (R={(a,b):a\leq b}). Why is (R) not symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn A = {1,2,3,4}, let R = {(a,b) : a + b ≤ 5}. Is R symmetric?Class 12Relations and FunctionsSymmetric relationLevel 12MediumMathematicsOn (A={1,2,3}), (R={(a,b):a^2=b^2}). What type of relation is (R)?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsIf the directed graph of a relation has an arrow from (x) to (y), what is necessary for the relation to be symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsIf (R) is symmetric and ((a,b)\notin R), must ((b,a)\notin R) also be true?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn (A={1,2,3,4}), a symmetric relation (R) has exactly (2) diagonal pairs and exactly (2) off-diagonal mirror-pair groups. How many such relations are possible?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Why is (R) not symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn A = {1,2,3}, let R = {(1,1),(2,2),(3,3),(1,2),(2,1)}. Choose the correct statement.Class 12Relations and FunctionsSymmetric relationLevel 12MediumMathematicsOn (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). What is the correct statement about (R)?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn A = {1,2,3,4}, let R = {(a,b) : a + b = 5}. What type of relation is R?Class 12Relations and FunctionsSymmetric relationLevel 12MediumMathematicsIf R is a symmetric relation, which statement about R ∪ R⁻¹ is correct?Class 12Relations and FunctionsSymmetric relationLevel 12MediumMathematicsOn (A={1,2,3}), how many symmetric relations contain ((1,2)) but do not contain ((1,1))?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsIf A has n elements, how many symmetric relations on A contain no diagonal pair (a,a)?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn (A={1,2,3,4}), (R={(a,b):a\mid b}). Which is the correct counterexample showing that (R) is not symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn (A={1,2,3,4,5}), (R={(a,b):a\equiv b \pmod{2}}). Why is (R) symmetric?Class 12Relations and FunctionsSymmetric relationLevel 10HardMathematicsOn (A={1,2,3,4}), (R={(a,b):|a-b|=1}). Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 10Hard