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Equivalence

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}, let R = {(a,b) : a^2 = b^2}. What type of relation is R?Class 12Relations and FunctionsEquivalence relationLevel 25Medium MathematicsOn (A=\mathbb{R}), (xRy) if (\sin x=\sin y). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) if (a) and (b) lie in the same block among ({1,2}), ({3,4,5}), ({6,7,8}). How many pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn natural numbers, (aRb) if (a) and (b) have the same sum of digits. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsIf two equivalence classes ([a]) and ([b]) of an equivalence relation are distinct, what is true about their intersection?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4}), an equivalence relation has the single class ({1,2,3,4}). Which relation is it?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn real numbers, (xRy) if (x^3=y^3). What is the correct conclusion about this relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A=\mathbb{R}), (xRy) if (x-y=0). Which relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)}). Is (R) an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) if (a\equiv b \pmod{3}). How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A=\mathbb{R}), (xRy) if (|x|=|y|). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsIf (f:A\to B) is a function and (aRb) if (f(a)=f(b)), what type of relation is (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsFor a non-empty set (A), which statement about the empty relation (\varnothing) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsFor a non-empty set (A), which statement about the universal relation (A\times A) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn real numbers, (xRy) if (x-y) is rational. Which statement about (R) is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if (a) and (b) leave the same remainder when divided by (2). How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn integers, (aRb) if (a^2\equiv b^2 \pmod{5}). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn natural numbers, (aRb) if (a) and (b) have the same number of prime factors, counted with repetition. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn real numbers, relation (R) is defined by ((x,y)\in R) if (x-y\in \mathbb{Z}). Which description is correct?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsFor natural numbers, (aRb) if (a) and (b) have the same last digit. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 16Easy