Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion(s) logically follow(s) from the given statements.

Statements:

All Grapes are Berries.

Some Berries are Juices.

All Juices are Sodas.

Conclusions:

(I) Some Berries are Grapes.

(II) Some Sodas are Berries.

To determine which conclusion(s) logically follow(s) from the given statements, we can analyze the relationships step-by-step using set theory or Venn diagrams.

Step 1: Analyze the Statements
1. "All Grapes are Berries." This means the set of Grapes is entirely contained within the set of Berries ($\mathrm{Grapes}\subseteq \mathrm{Berries}$).
2. "Some Berries are Juices." This means there is an intersection between the set of Berries and the set of Juices ($\mathrm{Berries}\cap \mathrm{Juices}\ne \varnothing$).
3. "All Juices are Sodas." This means the set of Juices is entirely contained within the set of Sodas ($\mathrm{Juices}\subseteq \mathrm{Sodas}$).

Step 2: Evaluate Conclusion (I) - "Some Berries are Grapes"
From Statement 1, we know that all Grapes are Berries. Since the set of Grapes is a subset of Berries, any element that is a Grape must also be a Berry. Thus, there exists at least some members of the Berry set that are Grapes. Therefore, Conclusion (I) logically and definitely follows.

Step 3: Evaluate Conclusion (II) - "Some Sodas are Berries"
From Statement 2, we know that there is a common region (intersection) between Berries and Juices. Let this common part contain some elements.
From Statement 3, all Juices are Sodas, meaning the entire set of Juices (including the part that overlaps with Berries) lies inside the set of Sodas.
Since the intersecting region of Berries and Juices is fully contained within Sodas, those Juices that are Berries must also be Sodas. Consequently, there must be an overlap between Sodas and Berries. Therefore, Conclusion (II) logically and definitely follows.

Conclusion:
Since both Conclusion (I) and Conclusion (II) are logically valid, the correct option is "Both the conclusions (I) and (II) follow".