66. Statements: 1. Some men are great. 2. Some men are wise. Conclusions: 1. Men are either great or wise. 2. Some men are neither great nor wise.
(A) If only Conclusion 1 follows
(B) If only Conclusion 2 follows
(C) If both Conclusions 1 and 2 follow
(D) If none of the Conclusion follows
Answer:
(D) If none of the Conclusion follows
Explanation:
In formal syllogistic logic, “Some” does not cover “All.” Since we only know that some men are great and some are wise, we cannot definitively conclude that all men fall into one of these two categories, nor can we formally prove the negative existence of a third group based solely on the given premises.
67. Statements: 1. All players are doctors. 2. Some doctors are actors. Conclusions: 1. Some doctors are players as well as actors. 2. All actors are doctors.
(A) If only Conclusion 1 follows
(B) If only Conclusion 2 follows
(C) If both Conclusions 1 and 2 follow
(D) If none of the Conclusion follows
Answer:
(D) If none of the Conclusion follows
Explanation:
The overlap between “players” and “actors” is unknown because the “doctors who are actors” might not be the same subset as the “doctors who are players.” Additionally, only some actors are known to be doctors. Therefore, neither conclusion is strictly valid.
68. Statements: 1. All saters [skaters] are good swimmers. 2. All good swimmers are runners. Conclusions: 3. Some runners are skaters. 4. Some skaters are good swimmers.
(A) If only Conclusion 1 follows
(B) If only Conclusion 2 follows
(C) If both Conclusions 1 and 2 follow
(D) If none of the Conclusion follows
Answer:
(C) If both Conclusions 1 and 2 follow
Explanation:
If all skaters are good swimmers, and all good swimmers are runners, then all skaters must be runners. Therefore, it is true that some runners are skaters (Conclusion 1). Furthermore, since all skaters are good swimmers, it is also true that some skaters are good swimmers (Conclusion 2).
69. Statements: 1. Some buses are four wheelers. 2. All four wheelers are vans. Conclusions: 1. Some vans are buses. 2. Some buses are vans.
(A) If only Conclusion 1 follows
(B) If only Conclusion 2 follows
(C) If both Conclusions 1 and 2 follow
(D) If none of the Conclusion follows
Answer:
(C) If both Conclusions 1 and 2 follow
Explanation:
Since some buses are part of the four-wheeler group, and every four-wheeler is a van, those specific buses must also be vans. This implies that some buses are vans, which conversely means some vans are buses. Both conclusions logically follow.
70. Statements: 1. All crows are birds. 2. All peacocks are crows. Conclusions: 1. All peacocks are birds. 2. All birds are peacocks.
(A) If only Conclusion 1 follows
(B) If only Conclusion 2 follows
(C) If both Conclusions 1 and 2 follow
(D) If none of the Conclusion follows
Answer:
(A) If only Conclusion 1 follows
Explanation:
Because all peacocks belong to the crow category, and all crows belong to the bird category, all peacocks must belong to the bird category (Conclusion 1). However, birds encompass more than just peacocks, making Conclusion 2 invalid.
