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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।

MathematicsWhich three properties are needed for a relation to be an equivalence relation?Class 12Relations and FunctionsTypes of relationsLevel 4EasyMathematicsIf (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)}) on (A={1,2,3,4}), which partition is formed by (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3HardMathematicsIf the only equivalence class of (R) on (A={1,2,3,4}) is ({1,2,3,4}), how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3HardMathematicsIf (aRb) on (A={1,2,3,4,5,6}) when (a\equiv b \pmod{2}), how many pairs are in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3HardMathematicsFor the partition ({{1,2},{3,4,5}}) of (A={1,2,3,4,5}), how many pairs are in the equivalence relation formed by it?Class 12Relations and FunctionsIntroduction to RelationsLevel 3HardMathematicsIf (R) on (A={1,2,3}) is reflexive and symmetric and ((1,2),(2,3)\in R), which pair is necessary to make (R) an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 2HardMathematicsOn (A={1,2,3,4}), if (aRb) when (|a-b|) is divisible by (2), what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2HardMathematicsFor the partition ({{1,2,3},{4}}) of (A={1,2,3,4}), how many pairs are in the equivalence relation formed by it?Class 12Relations and FunctionsIntroduction to RelationsLevel 2HardMathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}) on (A={1,2,3}), is (R) an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 3MediumMathematicsIf (R={(1,1),(2,2),(3,3),(4,4),(1,4),(4,1)}) on (A={1,2,3,4}), is (R) an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 3MediumMathematicsOn (A={1,2,3,4}), if (aRb) when (|a-b|) is even, what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3MediumMathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), why is (R) not an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 3MediumMathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}) on (A={1,2,3}), which pairs are still needed for equivalence?Class 12Relations and FunctionsIntroduction to RelationsLevel 3MediumMathematicsOn (A={1,2,3}), if (aRb) when (a+b) is even, which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsLevel 3MediumMathematicsIf on (A={1,2,3,4}), (aRb) if (a) and (b) are both even or both odd, what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 3MediumMathematicsIf (aRb) means (a) and (b) have the same parity, which conclusion is correct?Class 12Relations and FunctionsIntroduction to RelationsLevel 2MediumMathematicsOn (A={1,2,3,4}), if (aRb) when (a-b) is even, what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 2MediumMathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), which pairs are still needed for equivalence?Class 12Relations and FunctionsIntroduction to RelationsLevel 2MediumMathematicsIf (R={(1,1),(2,2),(3,3)}) on (A={1,2,3}), which statement about (R) is correct?Class 12Relations and FunctionsIntroduction to RelationsLevel 2MediumMathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), which conclusion is correct?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Medium