Q4. (4 pts, Set of Finite Binary Strings) Consider the following definition of binary strings: The set of finite binary strings, denoted by {0,1}^(*) which we read as "zero one star", is defined (recursively) by: Basis Step: lambda in{0,1}^(*) Recursive Step: If sin{0,1}^(*), then s0in{0,1}^(*) and s1in{0,1}^(*) where s0 and s1 are the results of solutionspile.com

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Q4. (4 pts, Set of Finite Binary Strings) Consider the following definition of binary strings: The set of finite binary strings, denoted by

{0,1}^(*)

which we read as "zero one star", is defined (recursively) by: Basis Step:

\lambda in{0,1}^(*)

Recursive Step: If

sin{0,1}^(*)

, then

s0in{0,1}^(*)

and

s1in{0,1}^(*)

where

s0

and

s1

are the results of string concatenation. The symbol

\lambda

, pronounced "lambda" is used to denote the empty string and has the property that

\lambda x=x\lambda =x

for each string

x

. Determine and justify whether the set

{0,1}^(*)

is finite, countably infinite, or uncountable.

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