Two statements are followed by four conclusions numbered I, II, III, IV. You have to take the given statements to be true even if…

Question

Two statements are followed by four conclusions numbered I, II, III, IV. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts:

Statements

1. All stars are planets.

2. All planets are trees.

Conclusions

I. All planets are stars

II. All stars are trees

III. All trees are planets

IV. Some trees are stars

Which of the conclusions follows logically?

1. A. Only II and IV follow (Correct answer)
2. B. Only I and II follow
3. C. All follow
4. D. Only III and IV follow

Correct Answer

Option A — Only II and IV follow

Detailed Solution & Explanation

The correct answer is Only II and IV follow.

Key Points

• The statements are: All stars are planets and All planets are trees.
• Conclusion II — All stars are trees: valid. Stars are contained within planets, and planets within trees, so stars are contained within trees by transitivity.
• Conclusion IV — Some trees are stars: valid. Since all stars are trees and the class of stars is non-empty, at least some trees must be stars — this is the legitimate converse of a universal affirmative.
• Conclusion I — All planets are stars: invalid. The original statement runs stars → planets, and reversing a universal affirmative is not permitted.
• Conclusion III — All trees are planets: invalid for the same reason; planets → trees cannot simply be reversed.

Additional Information

• Represented as nested circles: stars ⊂ planets ⊂ trees. Any conclusion reading from the inner circle outward is valid; any reading from the outer circle inward is not.
• Standard syllogism rule: "All A are B" always yields "Some B are A", but never "All B are A".