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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।

MathematicsOn (A={1,2,3,4}), how many pairs are in (R={(a,b):a-b\equiv0\pmod2})?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4,5}), (R={(a,b):a+b\equiv0\pmod 3}). Which property does this relation satisfy?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4,5}), (aRb) iff (a\equiv b\pmod 3). How many equivalence classes are formed?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4,5,6}), (aRb) iff (a) and (b) leave the same remainder on division by (2). How many equivalence classes are formed?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4}), (R={(a,b):a+b) is odd(}). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (ab\ge0). In which property does this relation fail?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (ab>0). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a-b>1). Which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (|a-b|<1). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (|a-b|\le 1). In which property does this relation fail?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a^3-b^3=0). What is the equivalence class of (2)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a^2-b^2=0). What is the equivalence class of (3)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a-b\in\mathbb{Q}). Which of the following classes is equal to ([0])?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a-b\in\mathbb{Q}). What is the equivalence class of (\sqrt{2})?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a-b\in\mathbb{Z}) and (a+b\in\mathbb{Z}). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (a+2b) is divisible by (4). Which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (2a+3b) is divisible by (5). In which property does this relation fail?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A={1,2,3,4}), how many equivalence relations have (1) and (2) in different classes?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A={1,2,3,4}), how many equivalence relations have (1) and (2) in the same class?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4,5}), how many equivalence relations have exactly three equivalence classes?Class 12Relations and FunctionsIntroduction to RelationsExpert