It is not the case that some physicians are either on the golf course or in the hospital. All of the neurologists are physicians in the hospital. Either some physicians are cardiologists or some physicians are neurologists. Therefore, some cardiologists are not on the golf course. (P, G, H, N, C )

Translate the following arguments into symbolic form. Then use the quantifier negation rule and the eighteen rules of inference to derive the conclusion of each. Do not use either conditional proof or indirect proof.