Suppose S is an infinite set. Assuming that the axiom of choice holds,

which of the following is true?

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Correct option is C

Result : necessary condition required for two sets to be in bijection is that there cardinality is same .

Now,

(i) Let S = R(set of real numbers) , then it cannot be in bijection with set of rational numbers as cardinality of set of rational numbers is less than that of real numbers .

(ii) Let S = Q (set of rationals) then option 2nd will also be incorrect .