Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow(s) from the given statements.
Statements:
(1)Some pencils are lanterns
(2)All lanterns are rubbers
(3)Some candies are pencils.
Conclusions:
(I) Some candies are lanterns
(II) Some rubbers are candies
(III) All pencils are rubbers

​Statements:
(1)Some pencils are lanterns.
(2)All lanterns are rubbers.
(3)Some candies are pencils.

Let's analyze the conclusions:

(I) Some candies are lanterns.

There is no direct relationship between candies and lanterns in the statements. While candies and pencils overlap, and pencils and lanterns overlap, this does not guarantee that candies and lanterns overlap.
 So Conclusion I doesn't follow.

(II) Some rubbers are candies.

Since some candies are pencils (Statement 3) and some pencils are lanterns (Statement 1), and all lanterns are rubbers (Statement 2), it doesn't possibility for candies to have an overlap with rubbers.
 So Conclusion II doesn't follow follows.

(III) All pencils are rubbers.

From Statements 1 and 2, we know that some pencils are lanterns and all lanterns are rubbers. However, there is no information that confirms all pencils are rubbers.
 and also Conclusion III doesn't follow.

Thus, the correct option is (c) None of the conclusions follow.