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Equivalence Class

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}, for aRb when a ≡ b (mod 3), what is the equivalence class [2]?Class 12Relations and FunctionsEquivalence relationLevel 25Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if (a) and (b) leave the same remainder on division by (3). What is ([2])?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsIf (R) is an equivalence relation and ((a,b)\in R), which statement is necessarily true?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={-2,-1,0,1,2}), (xRy) if (x^2=y^2). What is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A=\mathbb{Z}), (aRb) if (a-b) is divisible by (6). What is the equivalence class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4,5}), one equivalence class of (R) is ({1,2,5}). If (R) is an equivalence relation, which pair cannot be in (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if (\gcd(a,6)=\gcd(b,6)). What is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4}), the equivalence classes are ({1,4}) and ({2,3}). Which pair must belong to the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) if (a\equiv b \pmod{4}). What is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4}), relation (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)}) is given. What is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn positive integers, (aRb) if and only if (a) and (b) have the same power of (2), that is, (a=2^k m) and (b=2^k n), where (m,n) are odd. What forms the equivalence class of (12)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn all positive real numbers, (aRb) if and only if (\frac{a}{b}) is an integral power of (2). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn all real numbers, (aRb) if and only if (\cos^2 a=\cos^2 b). Which of the following must be in the equivalence class of (\frac{\pi}{3})?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn all real numbers, (aRb) if and only if (\sin^2 a=\sin^2 b). Which of the following numbers belongs to the equivalence class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn all real numbers, (aRb) if and only if (a^2-a=b^2-b). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same product of digits. Which number belongs to the equivalence class of (23)?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsIf (R) is an equivalence relation and (a\not R b), which statement about ([a]) and ([b]) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsIf (R) is an equivalence relation on a set (A) and ([a]\subseteq[b]), what conclusion is definite?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn all points in (R^2), (P R Q) if and only if the two points are at the same distance from the origin. What does the equivalence class of ((6,8)) represent?Class 12Relations and FunctionsEquivalence relationLevel 18Expert MathematicsOn all points in (R^2), (P R Q) if and only if the two points have the same (x)-coordinate. What is the equivalence class of ((3,-2))?Class 12Relations and FunctionsEquivalence relationLevel 18Expert