$4.$ BGP $14$ pts

a$.5$ pts Draw the following the AS diagram implied by the following routing table at AS$3$

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|\}$

$\backslash$hline Prefix & Route $\backslash \backslash$

$\backslash$hline P$1$ & AS$4$ AS$2$ AS$1\backslash \backslash$

$\backslash$hline P$2$ & AS$1$ AS$5\backslash \backslash$

$\backslash$hline P$2$ & AS$4$ AS$5\backslash \backslash$

$\backslash$hline P$1$ & AS$2$ AS$1\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

b$.4$ pts Why is one reason AS$1$ might not advertise P$2$ to AS$2?$ What is another route for P$1$ that could theoretically exist but does not?

c$.4$ pts What AS is P $1$ in$?$ What about P $2?$