Syllogism sample question

Question

Statements: All books are files. Some files are pens. Conclusion: Some books are pens.

1. A. Definitely true
2. B. Definitely false
3. C. Cannot be determined
4. D. Only if all files are books

Correct answer

Option C: Cannot be determined

The statements say all books lie inside files, and some files are pens. They do not prove that the files which are pens include any books. The conclusion may be true in one diagram and false in another, so it cannot be determined.

Why the other options are wrong

• Definitely true over-assumes overlap between books and pens.
• Definitely false is too strong because the overlap is possible.
• Only if all files are books adds a condition not present in the statements.

Solution method

1. Translate each statement into the smallest set relationship it guarantees.
2. Keep existence statements separate unless another statement connects those exact groups.
3. Try to draw one valid counterexample to the conclusion; if you can, the conclusion is not certain.

Concept boundary

'All books are files' places books inside files. 'Some files are pens' proves that at least one file is a pen, but it does not place that object inside the book subset. The conclusion may happen in one drawing, yet a syllogism conclusion must hold in every valid drawing unless the question specifically asks about possibility.

Transfer practice

All doctors are graduates. Some graduates are artists. Does 'Some doctors are artists' necessarily follow?

Practice tip

In syllogism, possible overlap is not the same as definite overlap.

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