Three statements are given followed by two conclusions numbered I and II. 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 cobblers are masons.
No mason is an electrician.
Some electricians are plumbers.
Conclusions:
I. All plumbers can never be masons.
II. At least some electricians are cobblers.
- AOnly Conclusion II follows.
- BNeither Conclusion I nor II follows.
- COnly Conclusion I follows.
- DBoth Conclusions I and II follow.
Solution & Step-by-step Explanation
Let's analyze the statements:
"All cobblers are masons" → Cobbler set is completely inside Mason set.
"No mason is an electrician" → Mason set and Electrician set have no overlap. Consequently, Cobbler set and Electrician set also have no overlap.
"Some electricians are plumbers" → There is a guaranteed overlap between Electrician and Plumber sets.
Now let's evaluate the conclusions:
Conclusion I: "All plumbers can never be masons."
The part of plumbers that are electricians can never be masons because no electrician is a mason. Therefore, it is impossible for all plumbers to ever be masons. Thus, this statement is true and follows.
Conclusion II: "At least some electricians are cobblers."
Since no mason is an electrician and all cobblers are masons, no electrician can be a cobbler. Thus, this conclusion does not follow.
Hence, only Conclusion I follows.
"All cobblers are masons" → Cobbler set is completely inside Mason set.
"No mason is an electrician" → Mason set and Electrician set have no overlap. Consequently, Cobbler set and Electrician set also have no overlap.
"Some electricians are plumbers" → There is a guaranteed overlap between Electrician and Plumber sets.
Now let's evaluate the conclusions:
Conclusion I: "All plumbers can never be masons."
The part of plumbers that are electricians can never be masons because no electrician is a mason. Therefore, it is impossible for all plumbers to ever be masons. Thus, this statement is true and follows.
Conclusion II: "At least some electricians are cobblers."
Since no mason is an electrician and all cobblers are masons, no electrician can be a cobbler. Thus, this conclusion does not follow.
Hence, only Conclusion I follows.