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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={1,2,3,4,5,6}), 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 16HardMathematicsIf (A) has (5) elements and (R) is an equivalence relation with (13) pairs, what can be the class sizes?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsIf (R) is an equivalence relation on a (7)-element set and (R) has (19) ordered pairs. Which class-size pattern is possible?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsOn integers, (aRb) holds when (a^3\equiv b^3 \pmod{7}). Why is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsOn (A={1,2,3,4,5,6}), how many equivalence classes are formed by the relation (\max(a,4)=\max(b,4))?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsIf (R) is an equivalence relation and (aRb), (bRc), (cRd), which conclusion must be true?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsOn (A={1,2,3,4,5,6,7,8,9,10}), (aRb) holds when (a) and (b) have the same greatest common divisor with (10). How many equivalence classes are formed?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsOn real numbers, (aRb) holds when (\sin a=\sin b). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsOn integers, (aRb) holds when (a-b) is divisible by both (6) and (10). This is the same as congruence modulo which number?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsIf an equivalence relation on a (6)-element set has class sizes (3,2,1), how many pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsOn (A={1,2,3,4,5,6,7,8}), how many ordered pairs are in the relation defined by (\gcd(a,8)=\gcd(b,8))?Class 12Relations and FunctionsEquivalence relationLevel 16HardMathematicsOn (A={1,2,3,4,5}), (aRb) holds when (a) and (b) are both greater than (2) or both not greater than (2). Which partition is formed by this relation?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsIf (R) is an equivalence relation and (x\in[y]), which conclusion is correct?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{3}). How many pairs are in this relation?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsOn (A={1,2,3,4}), (aRb) holds when (a+b) is even. How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsOn integers, (aRb) holds when (a) and (b) are both even or both not even. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsFor the same partition ({1,6},{2,5},{3,4}), which pair will not belong to the relation?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsFor the partition ({1,6},{2,5},{3,4}) of (A={1,2,3,4,5,6}), which pair belongs to the corresponding equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsWhich statement correctly describes the connection between an equivalence relation and a partition?Class 12Relations and FunctionsEquivalence relationLevel 18MediumMathematicsWhich option gives the universal relation on (A={1,2})?Class 12Relations and FunctionsEquivalence relationLevel 18Medium