Q$4.(4$ 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: $in\{0,1{\}}^{*}$

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 $,$ pronounced "lambda" is

used to denote the empty string and has the property that $x=x=x$ for each string $x.$

Determine and justify whether the set $\{0,1{\}}^{*}$ is finite, countably infinite, or uncountable.