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Equivalence

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

MathematicsOn real numbers, (aRb) iff (a-b) is an integer. What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Expert MathematicsOn integers, (aRb) iff (a+2b) is divisible by (3). In which property does this relation fail?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Expert MathematicsOn (A={1,2,3,4}), how many equivalence relations have exactly one class of size (2) and all other classes singleton?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Expert MathematicsIf (R) is the universal relation on a non-empty set (A), which statement is always true?Class 12Relations and FunctionsIntroduction to RelationsLevel 3Hard MathematicsWhat is the smallest change needed to make R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)} an equivalence relation on A={1,2,3}?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}). Why is it not an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a) and (b) are both even or both odd(}). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). What is the main reason it is not an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsOn real numbers, (aRb) iff (a^2=b^2). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsOn real numbers, (aRb) iff (a-b) is rational. What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b) is even(}). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsWhich statement is always true for the universal relation on a set (A)?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsOn the set of integers, relation (R) is defined by (aRb) if (a-b) is divisible by (5). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsIf (R=A\times A) on (A={1,2,3}), which statement about (R) is correct?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Medium MathematicsOn the set of integers, (aRb) if (a-b) is divisible by (3). What type of relation is this?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Medium MathematicsIf on (A={1,2,3,4}), (aRb) when (a) and (b) are both even or both odd, which pair belongs to the relation?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium MathematicsWhich statement is correct about the universal relation on a non-empty set?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium