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Ordered Pairs

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

MathematicsA partition ({{a,c,d},{b}}) is given on (A={a,b,c,d}). Which pair will not belong to the equivalence relation formed from it?Class 12Relations and FunctionsEquivalence relationLevel 18Expert 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 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}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}). Why is this not an equivalence relation?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 (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a) and (b) are of the same type: both less than (4) or both greater than or equal to (4). How many ordered pairs are there?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn the set of all real ordered pairs, ((a,b)R(c,d)) if and only if (a+b=c+d). How can the equivalence class of ((2,5)) be written?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4,5}), the relation is (R={(a,b):a\equiv b \pmod{2}}). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn the set (R^2) of all ordered pairs, ((a,b)S(c,d)) if and only if (a+c=b+d). Is (S) an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}) is given. Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) if and only if (a) and (b) leave the same remainder when divided by (3). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}). Which partition is obtained from this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsA partition of (A={1,2,3,4}) is ({{1,4},{2},{3}}). How many ordered pairs will be in the equivalence relation formed by it?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) is given. Which pairs are definitely needed to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4,5,6}), relation (R) has classes ({1,2,3},{4,5},{6}). How many ordered pairs are not in (R)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsIf (A) has (6) elements and an equivalence relation has exactly (31) ordered pairs, what can be the class sizes?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6}), relation (R) has classes ({1,2,6},{3,5},{4}). Along with ((6,1)) and ((5,3)), which pair must be in (R)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={(1,1),(1,2),(2,1),(2,2),(3,2)}), (aRb) holds when the two ordered pairs have the same second component. Which is the equivalence class of ((1,2))?Class 12Relations and FunctionsEquivalence relationLevel 18Medium