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Reflexivity

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsOn (A={1,2,3,4,5,6}), (aRb) if (a+b) is divisible by (3). Why is this not an equivalence relation?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 MathematicsIf (R) is an equivalence relation, why can ([a]) not be empty?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf (R) is an equivalence relation, what is true about ([a]) for any (a\in A)?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsWhy is the empty relation (\varnothing) on (A={1,2,3}) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Medium MathematicsIf (R) is an equivalence relation, from which property do we get ((a,a)\in R)?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsOn (A={1,2,3,4}), (R={(a,b):|a-b|=1}). Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationLevel 10Hard MathematicsLet A={1,2,3,4,5} and define aRb if and only if a+b is odd. Which statement correctly describes this relation?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(3,4),(4,3)}). Which property fails immediately?Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsIf (R) is an equivalence relation, by which property is (aRa) true for every element (a)?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsA relation (R) contains both ((a,b)) and ((b,a)), where (a\ne b). Which property is not guaranteed by this information alone?Class 12Relations and FunctionsTypes of relationsLevel 4Medium MathematicsIf (R={(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), why is (R) symmetric but not an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsIf (R={(1,1),(2,2),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not reflexive?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Medium