Statements : All oceans are rivers. Some springs are rivers. All wells are springs. Conclusions : I. Some springs are oceans. II. Some wells are rivers. III. Some rivers are oceans. IV. No well is river.

None follows
Only either I or III, and IV follow
Only either II or IV, and III follow
All follow E. Only either II or IV, and I follow

The correct answer is: A. None follows

The first statement, “All oceans are rivers,” is a universal affirmative statement. The second statement, “Some springs are rivers,” is a particular affirmative statement. The third statement, “All wells are springs,” is a universal affirmative statement.

To form a valid conclusion, we need to use the rules of syllogism. The first rule of syllogism is that the middle term must be distributed in at least one of the premises. In this case, the middle term is “rivers.” The first premise distributes the middle term, but the second premise does not. Therefore, we cannot form a valid conclusion.

The second rule of syllogism is that the conclusion must have the same quality (affirmative or negative) as the premises. In this case, the premises are both affirmative, but the conclusion is negative. Therefore, we cannot form a valid conclusion.

The third rule of syllogism is that the conclusion must have the same quantity (universal or particular) as the premises. In this case, the premises are both universal, but the conclusion is particular. Therefore, we cannot form a valid conclusion.

Therefore, none of the conclusions follow.