Consider the following propositions and conclusions:
Propositions:
* Some garnets are stones.
* Some stones are diamond.
* No diamond is a gem.
Conclusions:
1. Some gems are pearls.
2. Some gems are diamond.
3. No gem is a diamond.
4. No gem is a garnet.
Choose the correct alternative:
- AOnly (i) and (ii) follows
- BOnly (iii) and (iv) follows
- COnly either (i) or (iv) and either (ii) or (iii) follows
- DOnly (iii)
Solution & Step-by-step Explanation
Let us evaluate each conclusion based on the rules of syllogism:
* Conclusion (i) references 'pearls', which are entirely unmentioned in the premises. Hence, it does not follow.
* The third premise states "No diamond is a gem". By immediate conversion, "No gem is a diamond" must be completely true. This makes conclusion (iii) valid and conclusion (ii) invalid.
* There is no direct connection establishing a boundary between 'gem' and 'garnet', meaning conclusion (iv) cannot be definitively deduced.
Therefore, only conclusion (iii) logically follows.
* Conclusion (i) references 'pearls', which are entirely unmentioned in the premises. Hence, it does not follow.
* The third premise states "No diamond is a gem". By immediate conversion, "No gem is a diamond" must be completely true. This makes conclusion (iii) valid and conclusion (ii) invalid.
* There is no direct connection establishing a boundary between 'gem' and 'garnet', meaning conclusion (iv) cannot be definitively deduced.
Therefore, only conclusion (iii) logically follows.