Statements:
Only a few lantern are candle
All candle are flames
No lantern is sparks

Conclusions:
I. All candle being lantern is a possibility.
II. Some flames are not sparks
III. No sparks is candle

In each question below, some statements are given followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows.

The correct answer is Both I and II.

Let's analyze the statements step-by-step using standard syllogism and Venn diagram concepts:

Given Statements:
1. Only a few lantern are candle: This statement implies two things:
- Some lanterns are candles.
- Some lanterns are not candles.
Note that it does not restrict all candles from being lanterns. It only restricts all lanterns from being candles.
2. All candle are flames: This means the set of candles is entirely inside the set of flames.
3. No lantern is sparks: This means the set of lanterns and the set of sparks do not overlap at all (disjoint sets).

Now, let's evaluate each conclusion based on these statements:

Conclusion I: All candle being lantern is a possibility.
Let's check if we can draw a diagram where all candles are inside the lantern circle without violating any rules.
- The constraint "Only a few lanterns are candles" requires that some lanterns are candles and some lanterns are NOT candles.
- If all candles are inside the lantern circle, it is still possible that there is a part of the lantern circle that remains outside the candle circle. Thus, "Only a few lanterns are candles" is not violated.
- Therefore, it is entirely possible for all candles to be lanterns.
Hence, Conclusion I follows.

Conclusion II: Some flames are not sparks.
Let's examine the relationship between flames, lanterns, and sparks:
- From Statement 2, "All candle are flames", and Statement 1, "Only a few lantern are candle", we know there is an intersection between candles and lanterns.
- Since all candles are flames, the common part of candles and lanterns is also a part of flames. In other words, there is definitely a portion of flames that overlaps with lanterns.
- From Statement 3, "No lantern is sparks", we know that no part of lanterns can overlap with sparks.
- Since the overlapping portion of flames and lanterns lies entirely inside lanterns, this specific portion of flames can never overlap with sparks.
- Therefore, there is a guaranteed portion of flames (specifically, the flames that are candles which are also lanterns) that are not sparks.
Hence, Conclusion II follows.

Conclusion III: No sparks is candle.
Let's check if this must be true:
- We know no lantern is a spark.
- We also know all candles are flames, and some candles are lanterns.
- However, the remaining part of the candles (or flames) that does not overlap with lanterns has no direct restriction from being sparks.
- We can easily draw a possible case where the spark circle overlaps with the candle circle (in the region outside lanterns).
- Since a possibility of overlap exists, the definite conclusion "No sparks is candle" does not necessarily hold true in all cases.
Hence, Conclusion III does not follow.

Thus, only conclusions I and II follow logically.