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 teacher is an engineer.
All architects are engineers.
Conclusions:
I. No teacher is an architect.
II. Some teachers are architects.
- AOnly conclusion II follows
- BOnly conclusion I follows
- CNeither conclusion I nor II follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
Let's break down the statements logically:
"All architects are engineers" means the entire set of Architects lies inside the set of Engineers.
"No teacher is an engineer" means the set of Teachers has absolutely no intersection with the set of Engineers.
Since the Architects set is entirely inside the Engineers set, and Teachers cannot overlap with Engineers, it is impossible for Teachers to overlap with Architects.
Therefore, No teacher is an architect is definitely true. (Conclusion I follows).
Conclusion II ("Some teachers are architects") is completely false.
"All architects are engineers" means the entire set of Architects lies inside the set of Engineers.
"No teacher is an engineer" means the set of Teachers has absolutely no intersection with the set of Engineers.
Since the Architects set is entirely inside the Engineers set, and Teachers cannot overlap with Engineers, it is impossible for Teachers to overlap with Architects.
Therefore, No teacher is an architect is definitely true. (Conclusion I follows).
Conclusion II ("Some teachers are architects") is completely false.