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Reflexivity Failure

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

MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (\min(a,b)) is odd. Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all real numbers, (aRb) if and only if (|a|<|b|). Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all real numbers, (aRb) if and only if (a-b) is irrational. Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4}), (aRb) if and only if (a+b) is prime. Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all real numbers, (aRb) if and only if (a^2+b^2=0). Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn positive real numbers, (aRb) if and only if (\frac{\ln a}{\ln b}) is defined and rational. Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all real numbers, (aRb) if and only if (|a|+|b|=0). Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (a+b=6). Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (\max(a,b)) is even. Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (\gcd(a,b)>1). Is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn the set (R^2) of all ordered pairs, ((a,b)S(c,d)) if and only if (a+c=b+d). Is (S) an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4,5}), (R) has classes ({1,2,3},{4,5}). Why is the complement of (R) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainder modulo (3). What type of relation is the complement of (R)?Class 12Relations and FunctionsEquivalence relationHard MathematicsWhich option gives a relation that is not reflexive?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn real numbers, (aRb) holds when (a-b) is irrational. Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn integers, (aRb) holds when one of (a) and (b) is even and the other is odd. Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn (A={1,2,3,4}), why is (R={(1,1),(2,2),(4,4),(1,2),(2,1)}) not an equivalence relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn integers, (aRb) holds when (a+b) is odd. Why is it not an equivalence relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(2,3),(3,1)}). Why does reflexivity fail?Class 12Relations and FunctionsReflexive relationEasy