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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 = {1,2,3}, let R = {(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}. Which pair or pairs must be added to make R an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 26Hard MathematicsIf R is an equivalence relation on a set A, which statement about its equivalence classes is correct?Class 12Relations and FunctionsEquivalence relationLevel 25Medium MathematicsOn A = {1,2,3,4}, let R = {(a,b) : a^2 = b^2}. What type of relation is R?Class 12Relations and FunctionsEquivalence relationLevel 25Medium MathematicsOn A = {1,2,3,4,5}, R = {(1,2), (2,3), (4,5)}. How many ordered pairs are in the smallest equivalence relation containing R?Class 12Relations and FunctionsEquivalence relationLevel 27Hard MathematicsHow many equivalence relations on a 4-element set have exactly 2 equivalence classes?Class 12Relations and FunctionsEquivalence relationLevel 27Hard MathematicsOn A = {1,2,3,4,5}, for aRb when a ≡ b (mod 3), what is the equivalence class [2]?Class 12Relations and FunctionsEquivalence relationLevel 25Hard MathematicsIf an equivalence relation on (A={1,2,3}) contains ((1,2)) and ((2,3)), what is the minimum number of pairs in (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn integers, (aRb) if (a+b) is divisible by (2). Which statement is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsA relation (R) on a set (A) is reflexive and symmetric but not transitive. Which conclusion about (R) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsIf (R) and (S) are both equivalence relations on a set (A), which statement about (R\cap S) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsA partition of (A={1,2,3,4,5}) is ({{1,3,5},{2,4}}). How many ordered pairs will be in the equivalence relation formed by this partition?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsIf (R={(a,b):a+b\text{ is even}}) is defined on the set of integers, which statement about (R) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn the set (A={1,2,3,4,5,6}), relation (R) is defined by ((a,b)\in R) if (a-b) is divisible by (3). How many equivalence classes does this relation have?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn all real numbers, (aRb) if and only if (a^2+2a=b^2+2b). Which is the equivalence class of (-1)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn the set of all persons, (xRy) if and only if (x) and (y) have the same height. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn all triangles, (T_1RT_2) if and only if the two triangles have the same perimeter. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsIf the quotient set of an equivalence relation on (A) is (A/R={{1,4},{2,3,5}}), how many ordered pairs are in (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn (A={1,2,3,4,5}), (R={(1,1),(2,2),(3,3),(4,4),(5,5),(1,2),(2,1),(2,3),(3,2)}). Which minimum pairs must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Expert 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