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Introduction To Relations

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

MathematicsIn ({1,2,3,4,5,6}), how many equivalence classes are formed by the relation of having the same remainder on division by (3)?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIn the same-parity relation on ({1,2,3,4}), what is the equivalence class of (1)?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (R) is an equivalence relation and ((4,7)\in R), which pair must definitely be in (R)?Class 12Relations and FunctionsIntroduction to RelationsMedium 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 RelationsMedium MathematicsIf (R) is symmetric and transitive but not reflexive, is (R) an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf a relation (R) has domain ({1,2,3}) and range ({4,5}), what is the domain of (R^{-1})?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (R={(1,2),(2,3),(3,4)}), which of the following pairs must be added for a full transitive extension?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (R={(1,2),(2,1),(2,3),(3,2)}), which pair is first required by transitivity?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (R={(1,2),(2,3)}), which minimum pair must be added to complete transitivity?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (A={1,2,3}) and (R={(1,1),(2,3)}), which pairs must be added to make (R) reflexive?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (A={1,2,3}) and (R={(1,2),(3,3)}), what is the smallest relation needed to make (R) symmetric?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn real numbers, (aRb) means (a+b=0). Which property is correct?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn real numbers, (aRb) means (a-b>0). Which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn non-zero real numbers, (aRb) means (ab>0). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn real numbers, (aRb) means (a^2=b^2). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn integers, (aRb) means (|a|=|b|). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn integers, (aRb) means (a-b) is divisible by (3). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn integers, (aRb) means (a+b) is even. What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn natural numbers, (aRb) means (a\mid b). Which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsOn natural numbers, (aRb) means (a<b). Which property is correct?Class 12Relations and FunctionsIntroduction to RelationsMedium