Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: Some Toys are Plastic. Some Plastic are Metal. No Metal is Chemical. Conclusions: (I) Some Chemicals are Plastic. (II) No Toy is a Chemical.

Correct — C. Rule: a conclusion follows only if it is true in every diagram the statements allow.

Conclusion (I), Some Chemicals are Plastic, is only a possibility. Draw the Chemical circle clear of Plastic altogether and all three statements still hold, so (I) is not forced.

Conclusion (II), No Toy is a Chemical, is not forced either. Nothing in the statements links Toy to Chemical, so a Toy that is also a Chemical breaks nothing.

Neither conclusion is certain, so the answer is option (c).

Why the others are wrong

• (a)
  Only conclusion (I) follows. — Only (I) follows is wrong because (I) is merely possible. What the statements do force is that some Plastic are not Chemical, which is a different claim.
• (b)
  Both conclusions (I) and (II) follow. — Both follow needs each conclusion to be forced, and neither is. (II) in particular is a universal negative pulled out of two particular statements about Toys and Plastic.
• (d)
  Only conclusion (II) follows. — Only (II) follows fails because no statement connects Toy and Chemical. Toys may overlap Plastic and Plastic may overlap Metal, and none of that fences Toys away from Chemicals.

Syllogism items ask what must be true, not what could be. A conclusion follows only when every arrangement consistent with the statements contains it.

Two of the three statements here are particular — Some Toys are Plastic, Some Plastic are Metal — and a particular statement guarantees an overlap somewhere without saying where.

The one universal statement, No Metal is Chemical, separates Metal from Chemical. It says nothing about Toys, and Toy never touches Metal in any statement.

Key facts

• A conclusion follows only if it holds in every diagram the statements permit.
• Some Plastic are Metal together with No Metal is Chemical yields Some Plastic are not Chemical.
• No statement links Toy to Chemical, so neither an overlap nor a separation between them is forced.

Common traps

• Reading Some Plastic are Metal as licensing Some Chemicals are Plastic.
• Chaining Toy to Chemical through Plastic and Metal when both links are particular.
• Answering from a single Venn diagram instead of testing an alternative one.

No directly related past PYQ was found.