Consider the following function $p,$ where $L$ is a list.

B$.$ If $L=x,$ a single element, then $p(L)=x.$

R$.$ If $L=L^{\text{'}},x$ for some list $L^{\text{'}},$ then $p(L)=x,p(L^{\text{'}})".$

$($a$)$ If $L=$ john, paul, george, ringo, what is $p(L)?$

$($b$)$ What does the function $p$ do$,$ in general?

$($c$)$ Prove your assertion in part $($b$),$ using induction.