$($a$)$ Construct formal proofs Conditional Proof. of validity for the following argument, using the rule of

professors are learned. All learned professors are savants. Therefore all $4$S$-1$ All are learned professors

savants." $($Px$,$ Lx$,5$ x$)$ HAM $(2$ marks$)$

$($b$)$ Using quantification theory, prove that the following argument is invalid. Win Some pointers are spaniels because some dogs are pointers and some dogs are spaniels.