1. No objects that sink in water are chunks of ice, and no objects that float in water are things at least as dense as water. Accordingly, all chunks of ice are things less dense than water.

2. Some proposed flights to Mars are inexpensive ventures, because all unmanned space missions are inexpensive ventures, and some proposed flights to Mars are not manned space missions.

3. All schools driven by careerism are institutions that do not emphasize liberal arts. It follows that some universities are not institutions that emphasize liberal arts, for some schools that are not driven by careerism are universities.

4. No cases of encephalitis are infections easily curable by drugs, since all diseases that infect the brain are infections not easily curable by drugs, and all diseases that do not infect the brain are cases other than encephalitis.

5. Some foreign emissaries are people without diplomatic immunity, so some people invulnerable to arrest and prosecution are foreign emissaries, because no people with diplomatic immunity are people vulnerable to arrest and prosecution.

Rewrite the following arguments using letters to represent the terms, reduce the number of terms, and put the arguments into standard form. Then test the new forms with Venn diagrams or by means of the five rules for syllogisms to determine the validity or invalidity of the original arguments.