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Reflexive 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}), (R={(a,b):\gcd(a,b)=1}) is given. Is (R) reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a\text{ divides }b}). Which statement about (R) is correct?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (P(A)), (R={(X,Y):X \subset Y}), where (\subset) denotes proper subset. Which statement is correct about (R)?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn the power set (P(A)) of a set (A), the relation (R={(X,Y):X \subseteq Y}) is given. What is (R)?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (A={2,4,6}), (R={(a,b):a<b}). Why is (R) not reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (A={2,4,6}), (R={(a,b):a \le b}). Why is (R) reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b\text{ is odd}}). What is the correct conclusion about (R)?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (A={1,2,3,4,5}), (R={(a,b):a-b\text{ is divisible by }4}). Is (R) reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}) is given. Which statement about (R) is correct?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsWhat is the smallest necessary extension that makes a relation (R) reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsIf (R) is a reflexive relation on a set (A), which statement about (R^{-1}) is correct?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsIf (R) and (S) are reflexive relations on the same set (A), which statement about (R \cap S) is correct?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsThe matrix of a relation on a three-element set is (\begin{bmatrix}1&0&1\1&0&0\0&1&1\end{bmatrix}). What is the minimum number of entries to change to make it reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn the set (A={p,q,r,s}), which of the following relations is definitely reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsIf (A) has (5) elements, how many reflexive relations have exactly (3) additional pairs apart from the diagonal pairs?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsIf a set (A) has (4) elements, how many reflexive relations can be formed on (A)?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn the set (A={1,2,3}), the relation (R={(1,1),(1,2),(2,2),(3,1)}) is given. Which pair must be added at minimum to make it reflexive?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn A = {1, 2, 3}, let R = (A × A) \ {(1, 2), (2, 3)}. What is R?Class 12Relations and FunctionsReflexive relationLevel 9Medium MathematicsOn A = {1, 2, 3}, let R = (A × A) \ {(2, 2)}. Which statement about R is correct?Class 12Relations and FunctionsReflexive relationLevel 9Medium MathematicsIf R and S are two reflexive relations on A, what can be said about R ∩ S?Class 12Relations and FunctionsReflexive relationLevel 9Medium