Consider the following statements:

1. Some planets are stars.
2. All stars are comets.
3. No comet is an astronaut.

Based on the above statements, which of the following conclusions logically follow?

I. Some planets being astronauts is a possibility.
II. At least some comets are planets.

Question

Consider the following statements:

1. Some planets are stars.
2. All stars are comets.
3. No comet is an astronaut.

Based on the above statements, which of the following conclusions logically follow?

I. Some planets being astronauts is a possibility.
II. At least some comets are planets.

Accepted Answer

**Solution:**

1. From the statements:
   - Some planets are stars.
   - All stars are comets.
   - No comet is an astronaut.

2. Since all stars are comets, and some planets are stars, it follows that some planets are also comets.

3. Conclusion I states: "Some planets being astronauts is a possibility."
   - Since no comet is an astronaut, and some planets are comets, planets that are comets cannot be astronauts.
   - However, the statement says "some planets being astronauts is a possibility," which means it is possible that some planets (not necessarily those that are comets) could be astronauts.
   - Therefore, conclusion I is possible.

4. Conclusion II states: "At least some comets are planets."
   - Since some planets are stars and all stars are comets, it implies some comets are planets.
   - Hence, conclusion II logically follows.

5. Both conclusions I and II follow from the given statements.

**Answer:** If both conclusions I and II are true

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