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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={(1,1),(2,2),(1,2),(2,1)}) on (A={1,2}), what is (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Medium MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,3)}) on (A={1,2,3}), why is (R) not an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Medium MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}), which missing pair prevents it from being an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsFor the equivalence relation on (A={1,2,3}) formed by the partition ({{1},{2,3}}), which pair will not be present?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsIf an equivalence relation gives the partition ({{1,2},{3}}), which pair must be in the relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsIf (R) is an equivalence relation and ((4,7)\in R), which pair must definitely be in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsIf (R) is an equivalence relation and ((1,2)\in R), ((2,3)\in R), which pair must definitely be in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsIf (R) is symmetric and transitive but not reflexive, is (R) an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsOn non-zero real numbers, (aRb) means (ab>0). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsOn real numbers, (aRb) means (a^2=b^2). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsOn integers, (aRb) means (|a|=|b|). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsOn integers, (aRb) means (a-b) is divisible by (3). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsOn integers, (aRb) means (a+b) is even. What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsOn integers, (aRb) means (a-b) is even. What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsIf (R={(1,1),(2,2),(1,2)}), why is it not an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Easy MathematicsIf (R={(1,1),(2,2),(1,2),(2,1)}), is it an equivalence relation on (A={1,2})?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Easy MathematicsIf a relation is reflexive and symmetric but not transitive, will it be an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Easy MathematicsWhich type of relation is reflexive, symmetric and transitive?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Easy MathematicsIf (R) is reflexive and symmetric but not transitive, what can be said about (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Easy MathematicsWhy is (R={(1,1),(2,2),(3,3),(1,2)}) not an equivalence relation on (A={1,2,3})?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Easy