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

Step 1: Lay out the statements.
All Polymers are Cakes; Some Plastics are not Cakes; All Plastics are Synthetic Fibers.
Step 2: Use the definite some-not statement.
Because some Plastics are not Cakes, those particular Plastics exist and lie outside Cakes.
Step 3: Check Conclusion I.
Those non-Cake Plastics are still Synthetic Fibers, since all Plastics are, so there exist Synthetic Fibers that are not Cakes. Conclusion I follows.
Step 4: Check Conclusion III.
All Polymers are Cakes, but the Plastics that are not Cakes can never be Polymers, so the Polymer set and Plastic set cannot coincide; No Polymer is a Plastic follows.
Step 5: Check Conclusions II and IV.
Nothing links Cakes with Synthetic Fibers in general, and nothing links Polymers with Synthetic Fibers, so II and IV are not guaranteed.
Step 6: Select the option.
Only I and III follow.
\[ \boxed{\text{Only I and III follow.}} \]