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GATE | GATE-CS-2014-(Set-3) | Question 26

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  • Difficulty Level : Medium
  • Last Updated : 11 Oct, 2021
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(A) A
(B) B
(C) C
(D) D

Answer: (C)

Explanation: Let ∑ ={a, b}

then ∑* = { ε, a, b, aa, ba, bb, ……………….}

“Set of all strings over any finite alphabet are Countable“. Therefore, ∑* is countable.
Since there exist an enumeration procedure using which all the string of the language can be generated, which means each string can be counted in finite number of steps.

So, ∑* is countably infinite But 2Σ* is Uncountable, which can be proved using Diagonalization Method. This theorem says-  “If ∑* is countably infinite then 2Σ* is Uncountable”.

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