Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No watch is a frame.
All frames are shields.
Conclusions:
I. No watch is a shield.
II. No shield is a watch.
III. Some shields are frames.
IV. All shields are frames.
- AOnly conclusion III follows
- BBoth conclusions I and IV follow
- COnly conclusion I follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
Let's evaluate each conclusion systematically:
The statement "All frames are shields" directly implies that the intersection of shields and frames contains all frames. Therefore, "Some shields are frames" is definitely true. Hence, Conclusion III follows.
"No watch is a frame" means watch and frame sets are completely disjoint. However, shields can overlap with watches outside the frame boundary. Thus, "No watch is a shield" and "No shield is a watch" are not necessarily true. Conclusions I and II do not follow.
"All shields are frames" is incorrect because shields is the larger container set, making IV invalid.
Therefore, only conclusion III follows.
The statement "All frames are shields" directly implies that the intersection of shields and frames contains all frames. Therefore, "Some shields are frames" is definitely true. Hence, Conclusion III follows.
"No watch is a frame" means watch and frame sets are completely disjoint. However, shields can overlap with watches outside the frame boundary. Thus, "No watch is a shield" and "No shield is a watch" are not necessarily true. Conclusions I and II do not follow.
"All shields are frames" is incorrect because shields is the larger container set, making IV invalid.
Therefore, only conclusion III follows.