$1$ Universal Preference

Suppose that preferences in a stable matching instance are universal: all $n$ jobs share the preferences $C_1>C_2>$cdots$>C_n$ and all candidates share the preferences $J_1>J_2>$cdots$>J_n.$

$($a$)$ What pairing do we get from running the algorithm with jobs proposing? Can you prove this happens for all $n?$

$($b$)$ What pairing do we get from running the algorithm with candidates proposing?

$($c$)$ What does this tell us about the number of stable pairings?