Two 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 goods are services.
No service is a duty.
Conclusions:
I. Atleast some goods are duties.
II. No good is a duty.
- ANeither conclusion I nor II follows
- BOnly conclusion I follows
- COnly conclusion II follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
1. Analyze the Statements:
"All goods are services" means the set of goods is completely inside the set of services.
"No service is a duty" means the set of services and the set of duties have no intersection (disjoint sets).
Evaluate Conclusion I: "Atleast some goods are duties."
Since all goods are inside services, and no service can be a duty, it is impossible for any good to be a duty. Thus, conclusion I does not follow.
Evaluate Conclusion II: "No good is a duty."
Since all goods lie entirely within services, and services are completely separated from duties, no good can ever be a duty. Thus, conclusion II definitely follows.
"All goods are services" means the set of goods is completely inside the set of services.
"No service is a duty" means the set of services and the set of duties have no intersection (disjoint sets).
Evaluate Conclusion I: "Atleast some goods are duties."
Since all goods are inside services, and no service can be a duty, it is impossible for any good to be a duty. Thus, conclusion I does not follow.
Evaluate Conclusion II: "No good is a duty."
Since all goods lie entirely within services, and services are completely separated from duties, no good can ever be a duty. Thus, conclusion II definitely follows.