The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some potatoes are tomatoes.
All tomatoes are onions.
Conclusions:
I. Some tomatoes are potatoes.
II. All onions are potatoes.
- AEither Conclusion I or II follows.
- BOnly Conclusion I follows.
- COnly Conclusion II follows.
- DBoth Conclusions I and II follow.
Solution & Step-by-step Explanation
Let's evaluate the statements logically:
Statement 1: "Some potatoes are tomatoes." This relationship is symmetric. If some A are B, then some B are A. Therefore, "Some tomatoes are potatoes" is unconditionally true. Thus, Conclusion I follows.
Statement 2: "All tomatoes are onions."
Let's look at Conclusion II: "All onions are potatoes." From the given parameters, we only know that onions enclose all tomatoes, and tomatoes intersect partially with potatoes. It is possible that some onions are potatoes, but we cannot assert that all onions are potatoes. Thus, Conclusion II does not follow.
Statement 1: "Some potatoes are tomatoes." This relationship is symmetric. If some A are B, then some B are A. Therefore, "Some tomatoes are potatoes" is unconditionally true. Thus, Conclusion I follows.
Statement 2: "All tomatoes are onions."
Let's look at Conclusion II: "All onions are potatoes." From the given parameters, we only know that onions enclose all tomatoes, and tomatoes intersect partially with potatoes. It is possible that some onions are potatoes, but we cannot assert that all onions are potatoes. Thus, Conclusion II does not follow.