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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।

MathematicsIf (R) is defined on integers by (aRb) when (a-b) is even, then what type of relation is (R)?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). Is it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsWhich three properties are required for a relation on a set to be called an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn the set (A={1,2,3}), the relation (R={(1,1),(2,2),(3,3)}) is given. What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn the set of integers, (aRb) if (|a|=|b|). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsOn (A={1,2,3,4}), how many equivalence classes are formed by the same parity relation?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsIf (R) is an equivalence relation, which statement is always true?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsIf (aRb) means (a) and (b) have birthdays on the same date, what type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsIf ((a,b)\in R) and ((b,c)\in R) always imply ((a,c)\in R), which property is this?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsFor a relation (aRb) if (a=b), what type of relation is it on any set?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsOn integers, (aRb) if (a-b) is even. What kind of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsIf (R) is an equivalence relation and ((a,b)\in R), ((b,c)\in R), which conclusion is correct?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsWhy is the empty relation on (A={1,2,3}) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsWhich three properties must a relation have to be an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsOn the set of students of a school, (aRb) if (a) and (b) study in the same class. Choose the correct option about transitivity of (R).Class 12Relations and FunctionsTransitive relationLevel 15Hard MathematicsIf (R) is an equivalence relation on a set, what can be said about its transitive property?Class 12Relations and FunctionsTransitive relationLevel 13Hard MathematicsWhich statement about equivalence relations and reflexive relations is correct?Class 12Relations and FunctionsReflexive relationLevel 8Hard MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (a=b) or both numbers are prime. What type of relation is it?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if both (a,b) are multiples of (3), or both are not multiples of (3). How many ordered pairs are in the relation?Class 12Relations and FunctionsTypes of relationsLevel 6Expert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (a\equiv b \pmod{3}). How many ordered pairs are in the relation?Class 12Relations and FunctionsTypes of relationsLevel 6Expert