Statements:

Some Bottles are Papers

Some Papers are pens

No Pen is Pencil.

Conclusions :

(I) Some Bottle are pencil

(II) No Bottle is pencil

(III) Some Bottle are pen

Either (I) or (II) follows

The correct answer is Option 4: Either (I) or (II) follows

Analysis of Statements

1. Some Bottles are Papers: There is an overlap between the set of 'Bottles' and 'Papers'.

2. Some Papers are Pens: There is an overlap between 'Papers' and 'Pens'. However, this does not give us any direct information or guaranteed overlap between 'Bottles' and 'Pens'.

3. No Pen is Pencil: The sets of 'Pens' and 'Pencils' are completely disjoint (they cannot overlap).\

(I) Some Bottle are Pencil: This is not definitely true because there is no direct relation given between Bottle and Pencil.

(II) No Bottle is Pencil- This is also not definitely true because the statements do not completely separate Bottles and Pencils. Since conclusion (I) and conclusion (II) are exact opposites of each other (“Some Bottle are Pencil” and “No Bottle is Pencil”), exactly one of them must follow, but both cannot follow together.

(III) Some Bottle are Pen: This does not definitely follow because:

• Some Bottles are Papers
• Some Papers are Pens

The word “some” may refer to different Papers, so we cannot conclude that Bottles are definitely Pens.

Hence, only Either (I) or (II) follows.