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Transitivity

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

MathematicsOn non-zero integers, (aRb) is defined when (a) divides (b). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationLevel 13ExpertMathematicsOn a set (A), the empty relation (R=\varnothing) is given. Is (R) transitive?Class 12Relations and FunctionsTransitive relationLevel 15HardMathematicsOn the integers, define aRb when a+b is even. Is R transitive?Class 12Relations and FunctionsTransitive relationLevel 15HardMathematicsIf (R) is missing a pair ((a,b)), does that alone prove (R) is not transitive?Class 12Relations and FunctionsTransitive relationLevel 14HardMathematicsOn real numbers, (aRb) if (a=kb), where (k) is a fixed positive real number. In which case will this relation always be transitive?Class 12Relations and FunctionsTransitive relationLevel 14HardMathematicsIf (R) and (S) are transitive and (R\subseteq S), which statement about (S\setminus R) is correct?Class 12Relations and FunctionsTransitive relationLevel 14HardMathematicsIf (S) is transitive and (R\subseteq S), is (R) always transitive?Class 12Relations and FunctionsTransitive relationLevel 13HardMathematicsIf (R) is transitive and (R\subseteq S), is (S) always transitive?Class 12Relations and FunctionsTransitive relationLevel 13HardMathematicsIn a relation like the previous one, what is the correct conclusion when every required pair is actually present?Class 12Relations and FunctionsTransitive relationLevel 13HardMathematicsIf a relation (R) contains ((1,2)), ((2,1)), ((1,1)), and ((2,2)), which pair is required because of ((1,2)) and ((2,1))?Class 12Relations and FunctionsTransitive relationLevel 15MediumMathematicsIf (R) is transitive, which statement is correct?Class 12Relations and FunctionsTransitive relationLevel 15MediumMathematicsIf (R) is transitive and ((p,q)\in R), ((q,r)\in R), ((r,s)\in R), which pair is obtained in the first step by transitivity?Class 12Relations and FunctionsTransitive relationLevel 14EasyMathematicsIf a relation (R) contains ((1,2)), ((2,3)), and ((3,1)), which pair is definitely required for transitivity?Class 12Relations and FunctionsTransitive relationLevel 14EasyMathematicsIf (R={(1,3),(3,2)}), (R) is not transitive because which pair is missing?Class 12Relations and FunctionsTransitive relationLevel 14EasyMathematicsA relation (R) contains ((5,7)) and ((7,9)). If (R) is transitive, which pair must definitely be present?Class 12Relations and FunctionsTransitive relationLevel 14EasyMathematicsIf a relation (R) contains ((2,4)) and ((4,6)), which pair must be present for transitivity?Class 12Relations and FunctionsTransitive relationLevel 14EasyMathematicsWhich pair of transitive relations gives a union that is not transitive?Class 12Relations and FunctionsTypes of relationsLevel 6ExpertMathematicsOn (A={1,2,3,4}), (R) is an equivalence relation. If (1R2) and (2R4), which statement is necessary?Class 12Relations and FunctionsTypes of relationsLevel 4ExpertMathematicsIf (R) is an equivalence relation and (aRb), (bRc), (cRd), which conclusion is necessary?Class 12Relations and FunctionsTypes of relationsLevel 4ExpertMathematicsWhich relation on A={1,2,3} is transitive but not symmetric?Class 12Relations and FunctionsTypes of relationsLevel 4Expert