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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 real numbers, (aRb) iff (a-b\in\mathbb{Q}). Which class is equal to ([\sqrt{2}])?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a-b\in\mathbb{Z}). What is the equivalence class of (\frac{1}{2})?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (a+b) is even. What is the equivalence class of (1)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (2a+2b) is divisible by (4). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (3a+4b) is divisible by (7). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (a-b) is divisible by (8). What is the equivalence class of (-3)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A={1,2,3,4,5}), how many equivalence relations have (1) and (2) in the same class but (3) not in that class?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A={1,2,3,4,5}), how many equivalence relations have (1,2,3) in the same class?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4,5,6}), how many equivalence relations have class sizes (2,2,2)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4,5,6}), how many equivalence relations have two classes both of size (3)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4,5}), how many equivalence relations have exactly two equivalence classes?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A) has (5) elements, what is the total number of equivalence relations on (A)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A) has (5) elements, how many relations are reflexive, symmetric and antisymmetric all together?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A) has (4) elements, how many symmetric and irreflexive but non-empty relations are there on (A)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A) has (5) elements, how many antisymmetric relations can be formed on (A)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3}), (R={(1,1),(1,2),(2,3),(3,3)}). Why is this relation not transitive?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3}), (R={(1,2),(2,1),(2,3)}). Which pair must belong to (R\circ R)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3}), (R={(1,2),(2,3)}). What is (R\circ R)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (R) is a transitive relation, which statement about (R\circ R) is always true?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (R) is a reflexive relation on (A), which statement about (R\circ R) is always true?Class 12Relations and FunctionsIntroduction to RelationsExpert