Reasoning

Syllogism: Possibility Cases: Practice Questions with Answers

11 practice questions on Syllogism: Possibility Cases, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Statements: No pen is a book. All books are tables. Possibilities: I. It is possible that some tables are pens. II. It is possible that all tables are pens.

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   Answer: Only possibility I is valid

   Solution:

   1. Tables include all the books, but could also include other members beyond just books — those other members could be pens, so "some tables are pens" is possible.
   2. But the book-tables can never be pens (since no pen is a book), so not every table can possibly be a pen — "all tables are pens" is ruled out.

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2. Q.2

   Statements: All pens are books. No book is a table. Possibilities: I. It is possible that some pens are tables. II. It is possible that all tables are pens.

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   Answer: Neither possibility is valid

   Solution:

   1. Since every pen is a book, and no book is a table, pens and tables can never overlap in any valid diagram — ruling out both "some pens are tables" and the stronger "all tables are pens."

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3. Q.3

   Statements: All pens are books. Some books are tables. Possibilities: I. It is possible that all pens are tables. II. It is possible that no pens are tables.

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   Answer: Both possibilities are valid

   Solution:

   1. Since pens are a subset of books, and only SOME books are tables, nothing forces any particular pen to be (or not be) among the table-books.
   2. If the pen-books happen to be exactly the table-books, all pens could be tables — possible. If the pen-books fall entirely outside the table-books, no pens are tables — also possible.

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4. Q.4

   Statements: No pen is a book. No book is a table. Possibilities: I. It is possible that some pens are tables. II. It is possible that no pens are tables.

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   Answer: Both possibilities are valid

   Solution:

   1. Both statements only constrain pens and tables relative to books — neither statement says anything about pens and tables directly.
   2. With no direct or transitive link between pens and tables, their circles are free to overlap partially, fully, or not at all — both "some pens are tables" and "no pens are tables" are consistent with the given statements.

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5. Q.5

   Statements: Some pens are books. No book is a table. Possibilities: I. It is possible that all pens are tables. II. It is possible that some pens are tables.

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   Answer: Only possibility II is valid

   Solution:

   1. Since books are never tables, any pen that is also a book cannot be a table — and "some pens are books" guarantees at least one such pen, so not every pen can possibly be a table, ruling out "all pens are tables."
   2. But pens outside that book-overlap aren’t constrained at all — some of them could be tables, making "some pens are tables" possible.

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6. Q.6

   Statements: Some pens are books. Some books are tables. Possibilities: I. It is possible that some pens are tables. II. It is possible that no pens are tables.

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   Answer: Both possibilities are valid

   Solution:

   1. The "books that are pens" and the "books that are tables" could be the same books (making some pens tables) or entirely different books (making no pens tables) — both are consistent with the statements.

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7. Q.7

   Statements: Some pens are books. All books are tables. Possibilities: I. It is possible that some pens are not tables. II. It is possible that all pens are tables.

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   Answer: Both possibilities are valid

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8. Q.8

   Statements: Some pens are books. All books are tables. Possibilities: I. It is possible that some pens are tables. II. It is possible that no pens are tables.

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   Answer: Only possibility I is valid

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9. Q.9

   Statements: All pens are books. All books are tables. Possibilities: I. It is possible that all pens are tables. II. It is possible that no pens are tables.

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   Answer: Only possibility I is valid

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10. Q.10

    Statements: No pen is a book. Some books are tables. Possibilities: I. It is possible that some pens are tables. II. It is possible that no pens are tables.

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    Answer: Both possibilities are valid

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11. Q.11

    Statements: All pens are books. All books are tables. Possibilities: I. It is possible that some tables are not pens. II. It is possible that no pens are tables.

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    Answer: Only possibility I is valid (every pen is forced to be a table by the chain, so II is impossible)

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