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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}), (aRb) holds when (a=b) or (a+b=5). How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsIf ([x]={1,4,7}) in an equivalence relation, which of the following pairs is definitely in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn integers, (aRb) holds when (a^2-b^2) is divisible by (3). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn natural numbers, (aRb) holds when (a) and (b) have the same sum of digits. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn real numbers, (aRb) holds when (|a-2|=|b-2|). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn non-zero real numbers, (aRb) holds when (\frac{1}{a}) and (\frac{1}{b}) have the same sign. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsIf an equivalence relation has class sizes (4) and (2), how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn (A={1,2,3,4}), why is (R={(1,1),(2,2),(4,4),(1,2),(2,1)}) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn integers, (aRb) holds when (a-b) is divisible by (9). Which is the equivalence class of (25)?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn the set of non-zero polynomials, (pRq) holds when (p) and (q) have the same degree. Which is the equivalence class of (x^2+1)?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf the classes of an equivalence relation on a set are ({1,2}), ({3,4,5}), and ({6}), what is true about ((2,5))?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsOn real numbers, (aRb) holds when (\lfloor a\rfloor=\lfloor b\rfloor). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsOn integers, (aRb) holds when (a) and (b) are both positive or both not positive. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf (A) has (5) elements and the sizes of the equivalence classes are (2,2,1), how many pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsFor lines in a plane, (lRm) holds when (l) and (m) are parallel or identical. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsOn natural numbers, (aRb) holds when (a) and (b) have the same number of digits. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf ([a]={2,5,8}) and the relation is an equivalence relation, which pair must surely belong to the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsWhich option gives an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf a relation always has ((b,a)\in R) whenever ((a,b)\in R), which property is this?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) are both multiples of (3) or both not multiples of (3). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 17Medium