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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।

MathematicsWhen is a relation (R) on a set (A) called an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsOn real numbers, (aRb) holds when (a-b=0). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsWhich property of an equivalence relation requires that if ((a,b)\in R) and ((b,c)\in R), then ((a,c)\in R)?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsOn the set (A={1,2,3}), the relation (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) is given. Which pair must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsOn the set of triangles, a relation is defined such that two triangles are related when they have the same area. What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsWhat is the safest stepwise method to check an equivalence relation in a school exam?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,4),(4,1)}). What is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsIf (R) is an equivalence relation, which type of missing part should not occur in (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn (A={1,2,3}), (aRb) when (a=b) or both are from (1) and (2). What type of relation is (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn (A={1,3,5,7}), (aRb) when (a+b) is even. What type of relation is (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn (A={2,4,6,8}), (aRb) when (a) and (b) are both divisible by (2). What type of relation is (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsIf (aRb), (bRc), and therefore (aRc) are true, which property is shown?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsIf both (aRb) and (bRa) are true, which property does this indicate?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsIf (R) is an equivalence relation on (A), with what will every element (a\in A) be related?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsThe set (A={1,2,3,4}) is divided into parts ({1}), ({2,4}), ({3}). What type of relation is formed from this partition?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn (A={0,1,2,3,4,5}), (aRb) when (a \equiv b \pmod{3}). What is the equivalence class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn integers, (aRb) when (a\equiv b \pmod{2}). Which classes are formed?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}). Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsWhat is the correct meaning of the transitive property in an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsWhat is the correct meaning of the symmetric property in an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Easy