1. Physicists are the only scientists who theorize about the nature of time, and Stephen Hawking certainly does that. Therefore, Stephen Hawking must be a physicist.

2. Whenever suicide rates decline, we can infer that people's lives are better adjusted. Accordingly, since suicide rates have been declining in recent years, we can infer that people's lives have been better adjusted in recent years.

3. Environmentalists purchase only fuel-efficient cars. Hence, Jeep Wranglers must not be fuel efficient, since environmentalists do not purchase them.

4. Whoever wrote the Declaration of Independence had a big impact on civilization, and Thomas Jefferson certainly had that. Therefore, Thomas Jefferson wrote the Declaration of Independence.

5. There are public schools that teach secular humanism. Therefore, since secular humanism is a religion, there are public schools that teach religion.

Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms to determine whether each is valid or invalid. See Section 4.7 for help with the translation.