Statements:
Only screens are big
Some screens are television
Some television is not movie

Conclusions:
I. Some big being movie is possibility
II. All big being television is a possibility

In each question below some statements are given followed by two conclusions numbered I and II. 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 from the given statements, disregarding commonly known facts. Give answer-

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

Let us analyze the given statements and conclusions step-by-step to understand the logical deduction.

Step 1: Understand the given statements
1. "Only screens are big": In syllogism logic, "Only A are B" translates to "All B are A", with the restriction that B cannot belong to any other set except A. Therefore, "Only screens are big" means:
- All big are screens.
- No big can ever be anything other than a screen (i.e., 'Big' cannot overlap with 'Television', 'Movie', or any other entity outside 'Screen').

2. "Some screens are television": There is an intersection between the set of 'Screens' and 'Television'.

3. "Some television is not movie": There exists at least some portion of 'Television' that does not overlap with 'Movie'.

Step 2: Evaluate Conclusion I
Conclusion I states: "Some big being movie is possibility".
From the statement "Only screens are big", the element 'Big' is restricted exclusively to 'Screens'. 'Big' cannot share any part with any entity outside of 'Screens'. Hence, 'Big' can never be 'Movie', even as a possibility.
Therefore, Conclusion I does not follow.

Step 3: Evaluate Conclusion II
Conclusion II states: "All big being television is a possibility".
Again, due to the rule of "Only screens are big", 'Big' is strictly restricted to 'Screens' and cannot overlap with 'Television'. Therefore, 'Big' being 'Television' is not possible.
Therefore, Conclusion II does not follow.

Conclusion:
Since neither Conclusion I nor Conclusion II logically follows from the given statements, the correct option is If neither conclusion I nor II follows.