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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 the set of non-zero real numbers, (aRb) if and only if (\frac{a}{b}>0). On what basis is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn integers, (aRb) if and only if (a+b) is even. Which of the following statements is correct?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set of all functions from (A={1,2,3}) to (A), (fRg) if and only if (f(1)=g(1)). Choose the correct statement about this relation.Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set of (2\times 2) real matrices, (A RB) if and only if (\det(A)=\det(B)). Why is this relation an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set of all straight lines in a plane, (lRm) if and only if (l) and (m) have the same slope. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set (A={1,2,3,4}), the relation (R={(a,b):a-b\text{ is divisible by }2}) is given. Choose the correct statement about this relation.Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsIf an equivalence relation has (2) classes on a (7)-element set, what is the maximum possible number of pairs in the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsIf an equivalence relation has (2) classes on a (7)-element set, what is the minimum possible number of pairs in the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5}), (R) has classes ({1,2,3},{4,5}). Why is the complement of (R) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5}), (R) has classes ({1,2},{3},{4,5}). How many pairs are in the complement of (R)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6,7}), (aRb) holds when (a+b=8) or (a=b). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6,7}), relation (R) has classes ({1,7},{2,6},{3,5},{4}). How many pairs are in (R)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsIf (R) is an equivalence relation and ([a]\setminus[b]\neq\varnothing), which conclusion is correct?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn the integers, aRb when a-b is divisible by 5, and aSc when a-c is divisible by 10. What is R∪S equal to?Class 12Relations and FunctionsEquivalence relationLevel 17Hard 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 MathematicsOn (A={1,2,3,4,5,6,7,8,9,10}), how many equivalence classes are formed by the relation (\tau(a)=\tau(b))?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6}), for the relation where (a+b) is divisible by (7) or (a=b), how many ordered pairs are there?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a) and (b) have the same divisibility status by (4) and by (2). How many equivalence classes are formed?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (\gcd(a,9)=\gcd(b,9)). How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6,7}), (aRb) holds when (a) and (b) have the same divisibility status by (3) and the same divisibility status by (2). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Hard