Syllogism — Books, Papers, Journals, and Calendars Statements: • All the books are papers. • Some papers are journals. • Some journals are calendars. Conclusions: (1) Some journals are books. (2) Some calendars are papers. (3) Some books are journals. (4) Some books are calendars.

Introduction / Context:
This item explores how multiple subset and “some” statements interact. The trap is to assume overlaps that are not guaranteed by the premises, especially when two separate “some” statements could refer to different subgroups.

Given Data / Assumptions:

• Bk ⊆ Pa (All books are papers).
• Some Pa are Jo (some papers are journals).
• Some Jo are Ca (some journals are calendars).
• Conclusions: (1) Some journals are books. (2) Some calendars are papers. (3) Some books are journals. (4) Some books are calendars.

Concept / Approach:
We must test whether a conclusion must be true in every model satisfying the premises. If a counterexample exists, that conclusion does not follow. Separate “some” statements may refer to disjoint elements unless a link forces the same individuals to be shared.

Step-by-Step Solution:

Verification / Alternative check:
Because nothing requires the “some papers that are journals” to be the same individuals as the “some journals that are calendars,” overlaps with books or calendars are not forced. Hence none of the conclusions must follow.

Why Other Options Are Wrong:

• (1), (3), (4) rely on an unforced overlap between Books and Journals (or Calendars).
• (2) assumes Journals that are Calendars must also be Papers; the premises do not require that.

Common Pitfalls:
Chaining separate “some” facts as if they refer to the same elements. Without an “all” or explicit identity, such chaining is invalid.

Final Answer:
None of the four