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option d ?
D. Set of all languages over a finite alphabet is countable (finitely or infinitely). Rest all options all incorrect.

Ans d is correct.

set of all integer is countable. Generate like 1, -1,2,-2... so for a number x. I will take 2x steps to generate it or the corresponding natural number will be 2x. And set of all strings is also countable .

Because (a) is incorrect due to there exist a one to one correspondence between natural no and sigma *

(b) is also incorrect because sigma* multiply as much time it remain same

(c) power set of every countable infinite set is always uncountable set

so d is correct option
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For countable set, is one-one mapping to integers necessary?

If not, then for option (D), I can map $\sum$* to set of integers as per their lengths.