Using rules of inference and propositional logic, prove that the premises "I fail this class only if I do not attend class today", "I am sick, or I attend class today", and "I am not sick" imply the conclusion "I pass this class."

$2.(2\mathrm{.}5$ marks$)$

Using rules of inference and predicate logic, prove that the premises "All lawyers are pedantic or incompetent" and "There is a lawyer who is not incompetent" imply the conclusion "There is a lawyer who is pedantic."