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GATE 2014 [Set-3]
April 4, 2025GATE 2014 [Set-3]
April 4, 2025GATE 2014 [Set-3]
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Question 26
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Let Σ be a finite non-empty alphabet and let 2Σ* be the power set of Σ*. Which one of the following is TRUE?
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Both 2Σ* and Σ* are countable
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2Σ* is countable and Σ* is uncountable
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2Σ* is uncountable and Σ* is countable
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Both 2Σ* and Σ* are uncountable
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Question 26 Explanation:
If = {0,1} then Σ* = {ϵ, 0, 1, 00, 01, 10, 11, 000, ……………}
Since we can enumerate all the strings of Σ*, hence Σ* is countable (countable infinite).
While 2Σ* is uncountable, it has been already proved by using Diagonalization method.
Since we can enumerate all the strings of Σ*, hence Σ* is countable (countable infinite).
While 2Σ* is uncountable, it has been already proved by using Diagonalization method.
Correct Answer: C
Question 26 Explanation:
If = {0,1} then Σ* = {ϵ, 0, 1, 00, 01, 10, 11, 000, ……………}
Since we can enumerate all the strings of Σ*, hence Σ* is countable (countable infinite).
While 2Σ* is uncountable, it has been already proved by using Diagonalization method.
Since we can enumerate all the strings of Σ*, hence Σ* is countable (countable infinite).
While 2Σ* is uncountable, it has been already proved by using Diagonalization method.