In this question, three 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 follows/follow from the statements.

Statements:

I.  No streak is a line.
II. Some lines are bands.
III. All bands are flashes.

Conclusions:

I.  Some flashes are streaks.      II.  No flash is a line.

To determine which of the conclusions logically follows from the given statements, we can analyze the relationships using a Venn diagram or syllogistic reasoning.

Let's analyze the given statements:
1. Statement I: "No streak is a line." - This means the set of "streaks" and the set of "lines" have no intersection (they are completely disjoint).
2. Statement II: "Some lines are bands." - This means there is an intersection between the set of "lines" and the set of "bands".
3. Statement III: "All bands are flashes." - This means the entire set of "bands" is contained within the set of "flashes". Since some "lines" are "bands" and all "bands" are "flashes", it logically follows that some "flashes" are "lines" (specifically, the portion of bands that overlap with lines).

Now let's evaluate each conclusion based on these relationships:
Conclusion I: "Some flashes are streaks."
From the statements, we know that no streak is a line, some lines are bands, and all bands are flashes. There is no direct or indirect constraint or positive connection given between the set of "flashes" and "streaks". It is possible that some flashes are streaks, but it is not definite or necessary. Therefore, conclusion I does not logically follow.

Conclusion II: "No flash is a line."
From Statement II ("Some lines are bands") and Statement III ("All bands are flashes"), we know that the overlapping region between "lines" and "bands" must also be part of "flashes". Therefore, there is definitely an intersection between "flashes" and "lines", meaning at least some flashes must be lines. This directly contradicts the conclusion "No flash is a line". Thus, conclusion II does not follow.

Since neither conclusion I nor conclusion II follows, the correct option is "Neither conclusion I nor II follows".