Directions: In the question below, some statements are given followed by two conclusions. Assume the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and decide which of the given conclusions logically follow(s) from the statements.

Statements:
Only Quartz is Amber.
Some Quartz is Garnet.
All Garnet is Crystal.

Conclusions:
I. All Amber can be Garnet
II. Some Crystal is not Quartz

The correct answer is If neither conclusion I nor II follows.

Step 1: Analyze the given statements
1. "Only Quartz is Amber": In syllogism logic, "Only A is B" means "All B is A", with the additional condition that B is exclusive to A. Therefore, "All Amber is Quartz" and Amber cannot overlap with any other element or set (such as Garnet or Crystal).
2. "Some Quartz is Garnet": There is a partial overlap between the category of Quartz and Garnet.
3. "All Garnet is Crystal": The complete set of Garnet is contained within the set of Crystal.

Step 2: Evaluate Conclusion I
Conclusion I: All Amber can be Garnet
Due to the exclusivity rule of "Only Quartz is Amber", Amber cannot belong to any set other than Quartz. Thus, Amber can never be Garnet.
Hence, Conclusion I does not follow.

Step 3: Evaluate Conclusion II
Conclusion II: Some Crystal is not Quartz
We know that all Garnet is Crystal and some Quartz is Garnet, which implies that some Crystal is Quartz. However, there is no restriction preventing the entire set of Crystal from being inside Quartz. Since it is possible for all Crystal to be Quartz without violating any given statements, we cannot definitively conclude that "Some Crystal is not Quartz".
Hence, Conclusion II does not follow.

Conclusion:
Neither conclusion I nor II logically follows from the given statements.