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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}), the relation is (R={(a,b):a\equiv b \pmod{2}}). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn integers, (aRb) if and only if (a^2-b^2) is divisible by (8). Which of the following pairs belongs to the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a-b) is divisible by (4). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn the set of all students, (xRy) if and only if (x) and (y) have the same date of birth. Why is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4,5,6,7}), (aRb) if and only if (a) and (b) leave the same remainder on division by (2). Which statement about ((4,7)) is correct?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set (R^2) of all ordered pairs, ((a,b)S(c,d)) if and only if (a+c=b+d). Is (S) an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set of all circles, (C_1RC_2) if and only if the two circles have the same radius. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsIf (A) has (5) elements and the partition of an equivalence relation is ({{a,b},{c,d,e}}), how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}) is given. Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set of all polynomials with real coefficients, (pRq) if and only if (p(0)=q(0)). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn real numbers, (aRb) if and only if (\sin a=\sin b). Is this relation an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) if and only if (a) and (b) leave the same remainder when divided by (3). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn real numbers, (aRb) if and only if (a^3=b^3). Choose the correct statement about this relation.Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set of real numbers, (aRb) if and only if (\lfloor a\rfloor=\lfloor b\rfloor). Which is the equivalence class of (2.4)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsIf (R) is an equivalence relation on a set (A), which statement is true about two distinct equivalence classes?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn the set of all triangles, (T_1RT_2) if and only if (T_1) and (T_2) are similar. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same unit digit. Which statement about this relation is correct?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsA partition of (A={1,2,3,4}) is ({{1,4},{2},{3}}). How many ordered pairs will be in the equivalence relation formed by it?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) is given. Which pairs are definitely needed to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) is given. Which minimum pair must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Expert