Below, $,,,$ are taken to be propositions.

a$)$ Use the semantic tableaux method to show that the following semantic implication holds:

$\{=>(((not(=>))=>)=>(not))\}||===>(not)$

b$)$ Write down a direct proof of the following syntactic implication $($a proof that does not assume the validity of any theorems and does not use the Deduction Theorem$)$:

$\{=>(((not(=>))=>)=>(not))\}|--|=>(not)$