Three statements are given, followed by three conclusions numbered I, II and III.
Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All papers are files.
Some files are maps.
No map is a paint.
Conclusions:
I. Some papers are files.
II. All maps are files.
III. Some maps are not paints.
- AOnly conclusion II and III follow
- BOnly conclusions I and II follow
- CAll of the conclusions follow
- DOnly conclusion I and III follow
Solution & Step-by-step Explanation
Let's analyze the conclusions step by step:
Conclusion I: "Some papers are files." Since "All papers are files" is given as true, "Some papers are files" must definitely be true. Thus, Conclusion I follows.
Conclusion II: "All maps are files." Statement 2 says "Some files are maps," which does not imply that all maps are files. Thus, Conclusion II does not follow.
Conclusion III: "Some maps are not paints." Statement 3 explicitly states "No map is a paint." If no map is a paint, then any subset of maps is also not a paint, meaning "Some maps are not paints" is definitely true. Thus, Conclusion III follows.
Therefore, only conclusions I and III follow.
Conclusion I: "Some papers are files." Since "All papers are files" is given as true, "Some papers are files" must definitely be true. Thus, Conclusion I follows.
Conclusion II: "All maps are files." Statement 2 says "Some files are maps," which does not imply that all maps are files. Thus, Conclusion II does not follow.
Conclusion III: "Some maps are not paints." Statement 3 explicitly states "No map is a paint." If no map is a paint, then any subset of maps is also not a paint, meaning "Some maps are not paints" is definitely true. Thus, Conclusion III follows.
Therefore, only conclusions I and III follow.