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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|). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a^2\le b^2). Which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a^3=b^3). What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a-b) is irrational. Which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn real numbers, (aRb) iff (a-b) is an integer. What type of relation is it?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (a+2b) is divisible by (3). In which property does this relation fail?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn integers, (aRb) iff (a-b) is divisible by (6). What is the equivalence class of (7)?Class 12Relations and FunctionsIntroduction to RelationsExpert 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 RelationsExpert MathematicsOn (A={1,2,3,4,5}), how many equivalence relations have one class of size (2) and the other of size (3)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsOn (A={1,2,3,4}), how many equivalence relations have exactly two equivalence classes?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A) has (4) elements, how many equivalence relations can be formed on (A)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsHow many relations on (A={1,2,3,4}) are reflexive, symmetric and antisymmetric all together?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsHow many relations on (A={1,2,3,4}) are both symmetric and antisymmetric?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A) has (5) elements, what is the number of relations on (A) that are both reflexive and antisymmetric?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (A) has (4) elements, how many antisymmetric relations can be formed on (A)?Class 12Relations and FunctionsIntroduction to RelationsExpert MathematicsIf (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}) on (A={1,2,3,4}), which statement about (R) is false?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R) is symmetric on (A={1,2,3}) and ((1,3)) is in (R\circ R), what type of chain may be possible?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf the classes of (R) on (A={1,2,3,4}) are ({1,2}) and ({3,4}), which pair must be in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (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 RelationsHard MathematicsOn (A={1,2,3,4}), if (aRb) when (a\le b), which statement is correct?Class 12Relations and FunctionsIntroduction to RelationsHard