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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.