$($a$)$ Is the set of formulae $\{$p$,$ p $->$ q$,$ q $->$ r$,$ r $->\}$ satisfiable? Prove your answer without using a truth table.

$($b$)$ True or False? For every pair of formulas A and B$,$ if A and A $->$ B are satisfiable then B is satisfiable. Prove your answer.