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Equivalence Relation

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

MathematicsOn a set with (8) elements, an equivalence relation has class sizes (2,2,4). How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn (A={1,2,3,4,5,6}), (R={(a,b):a) and (b) leave the same remainder on division by (3)(}). How many ordered pairs are in (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn (A={1,2,3,4,5,6,7,8,9,10,11,12}), (aRb) if and only if (a) and (b) leave the same remainder on division by (6). Which is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsWhich of the following relations on the set of integers \(\mathbb{Z}\) is an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsIf an equivalence relation has classes ({1,2}), ({3,4,5}), and ({6}), which statement about ((2,5)) and ((4,3)) is correct?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsIf (R) and (S) are equivalence relations, which statement is generally true about (R\cup S)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsIf (R) and (S) are equivalence relations on the same set (A), which statement about (R\cap S) is correct?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn the set of all rectangles, (R_1RR_2) if and only if the two rectangles have the same area. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn all real numbers, (aRb) if and only if (a-b) is an integer. Choose the correct statement about (0.25) and (3.25).Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}). Which relation is this?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsAn equivalence relation on a set (A) has class sizes (1,2,4). If (A) has (7) elements, how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn all integers, (aRb) if and only if (a) and (b) leave the same remainder on division by (10). Choose the correct statement about (27) and (-13).Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn all real numbers, (aRb) if and only if (e^a=e^b). What will the equivalence classes be like?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (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 17Expert MathematicsOn the set of all linear equations (ax+by+c=0), two equations are related if they represent the same line. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn the set of all non-zero polynomials, (pRq) if and only if (\deg(p)=\deg(q)). What forms the equivalence class of (x^2+1)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn all (2\times 2) real matrices, (A RB) if and only if (\operatorname{tr}(A)=\operatorname{tr}(B)). Why is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2)}) is given. Which minimum pairs must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn all non-zero real numbers, (aRb) if and only if (\frac{a}{b}\in Q). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 17Expert