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Identity Relation

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf R = {(a,b) ∈ A × A : a = b}, what is R called?Class 12Relations and FunctionsTypes of relationsLevel 26EasyMathematicsOn A = {1,2,3,4}, let R = {(a,b) : a^2 = b^2}. What type of relation is R?Class 12Relations and FunctionsEquivalence relationLevel 25MediumMathematicsOn a set (A), which is the smallest equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn (A={1,2,3,4}), the identity relation is (I_A={(1,1),(2,2),(3,3),(4,4)}). How many equivalence classes does it have?Class 12Relations and FunctionsEquivalence relationLevel 17ExpertMathematicsOn (A={1,2,3,4}), which is the smallest equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsOn (A={1,2,3,4}), (aRb) if and only if (a=b). How many equivalence classes does this relation have?Class 12Relations and FunctionsEquivalence relationLevel 16ExpertMathematicsIf (A) has (4) elements, how many equivalence relations have no two distinct elements in the same class?Class 12Relations and FunctionsEquivalence relationLevel 17HardMathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainder on division by (7). What is this relation?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsIf (A) has (6) elements and the identity relation is taken, how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsWhich option gives the identity relation on (A={1,2,3,4})?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsOn (A={1,2,3,4}), what are the equivalence classes of the identity relation (I={(1,1),(2,2),(3,3),(4,4)})?Class 12Relations and FunctionsEquivalence relationLevel 17MediumMathematicsIf (A) has (n) elements, how many equivalence classes are formed by the identity relation?Class 12Relations and FunctionsEquivalence relationLevel 16MediumMathematicsFor (A={1,2,3}), which statement is correct about the identity relation (I={(1,1),(2,2),(3,3)})?Class 12Relations and FunctionsEquivalence relationLevel 16MediumMathematicsIf (R={(a,a):a\in A}), how can (R) be identified?Class 12Relations and FunctionsEquivalence relationLevel 18EasyMathematicsFor a non-empty set (A), which statement is correct about the equality relation (R={(a,a):a\in A})?Class 12Relations and FunctionsEquivalence relationLevel 17EasyMathematicsWhat are the equivalence classes of the identity relation on a set?Class 12Relations and FunctionsEquivalence relationLevel 16EasyMathematicsWhich relation is called the identity relation?Class 12Relations and FunctionsEquivalence relationLevel 16EasyMathematicsOn a set (A), the identity relation (I={(a,a):a\in A}) is given. Choose the correct option about (I).Class 12Relations and FunctionsTransitive relationLevel 15HardMathematicsIf (R) is transitive, what about (R\cup\Delta), where (\Delta={(a,a):a\in A})?Class 12Relations and FunctionsTransitive relationLevel 14HardMathematicsWhich statement is correct about the identity relation (I={(a,a):a \in A}) on a set?Class 12Relations and FunctionsTransitive relationLevel 15Medium