Question

Study the following statements and conclusions carefully. Statements:

• All Polymers are Cakes.

• Some Plastics are not Cakes.

• All Plastics are Synthetic Fibers.
Conclusions:

• [I.] Some Synthetic Fibers are not Cakes.

• [II.] Some Cakes are Synthetic Fibers.

• [III.] No Polymer is a Plastic.

• [IV.] Some Polymers are Synthetic Fibers.
Options:

• A. Only I and III follow.
• B. Only I follows.
• C. Only I, II and III follow.
• D. Only I and IV follow.

Hint:

Whenever a statement says "Some A are not B" and all A belong to another set C, immediately conclude "Some C are not B". Such conclusions are always valid.

Answer 1

The Correct Option is A

Concept: In syllogism problems, conclusions must necessarily follow from the given statements. A conclusion is accepted only when it is true in every possible arrangement satisfying the statements. Given: \[ \text{All Polymers} \subseteq \text{Cakes} \] \[ \text{All Plastics} \subseteq \text{Synthetic Fibers} \] Some Plastics are not Cakes The third statement provides definite existence information and is the key statement for solving the question.

Step 1: Examine Conclusion I. Some Plastics are not Cakes. Also, All Plastics are Synthetic Fibers Therefore those Plastics which are not Cakes are definitely Synthetic Fibers. Hence, Some Synthetic Fibers are not Cakes Conclusion I follows.

Step 2: Examine Conclusion II. We know: All Polymers are Cakes and All Plastics are Synthetic Fibers No direct relationship is given between Cakes and Synthetic Fibers. Therefore it cannot be concluded that some Cakes are Synthetic Fibers. Conclusion II does not follow.

Step 3: Examine Conclusion III. All Polymers are Cakes. Some Plastics are not Cakes. Therefore those Plastics which are not Cakes can never be Polymers. Thus Polymer and Plastic cannot be the same set. Hence the conclusion No Polymer is a Plastic follows.

Step 4: Examine Conclusion IV. No statement connects Polymers with Synthetic Fibers. Therefore it cannot be concluded that some Polymers are Synthetic Fibers. Conclusion IV does not follow. Therefore only Conclusions I and III follow. \[ \boxed{\text{Answer = (A)}} \]