In both the questions below, we will consider functions defined over n Boolean features.

That is$,$ each example in our learning problem is a n$-$dimensional vector from $\{0,1\}$n$.$ We

will use the symbol x to denote an example and xi denotes its ith element. $($We will assume

that there is no noise involved.$)$

Consider the concept class C$1$ defined as follows: Each element of C$1$ is defined using a

fixed instance z in $\{0,1\}$n as follows:

f$\_$z$($x$)=$

$\{$

$1$ : x $=$ z

$0$ : x $!=$ z

$\}$

That is$,$ the function fz predicts $1$ if$,$ and only if$,$ the input to the function is z$.$

Our goal is to come up with a mistake bound algorithm that will learn any function

f in C$1.$

QUESTION: Determine $|$C$1|,$ the size of concept class.