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∑* over {0,1} and 2∑* are respectively,
  • a)
    Uncountably infinite and uncountably infinite
  • b)
    Countably infinite and uncountably infinite
  • c)
    Countably infinite and countably infinite
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
∑* over {0,1} and 2∑* are respectively,a)Uncountably infinite ...
Since ∑* is all the combinations of 0 and 1 and yet it is enumerable and belongs to the category of countably infinite. But 2∑* is the power set of ∑* which is infinite. By diagonalisation theorem, power set of any countably infinite set is always uncountable, hence 2∑*​ belongs to uncountably infinite set.
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∑* over {0,1} and 2∑* are respectively,a)Uncountably infinite and uncountably infiniteb)Countably infinite and uncountably infinitec)Countably infinite and countably infinited)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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