Pariksha SaathiSyllogism: Possibility Cases Questions with Solutions
A regular Syllogism conclusion has to hold in EVERY valid diagram to follow. A possibility conclusion only needs to hold in AT LEAST ONE valid diagram consistent with the statements — a much lower bar, and a different question entirely. Here’s the approach, four fully worked examples covering each pattern, and a few to try yourself.
The approach, quickly
- A possibility conclusion ("it is possible that...") is valid if you can draw even ONE diagram consistent with the statements where it holds — it does not need to hold in every diagram, unlike a regular "definitely follows" conclusion.
- A possibility conclusion is NOT valid only when it’s impossible in every single diagram consistent with the statements — meaning the statements actively rule it out, not just fail to guarantee it.
- Two "Some" statements, or a "Some" combined with another statement, usually leave real freedom in how the circles overlap — this is where both a positive and a negative possibility often turn out valid at once.
- When one category is fully nested inside another that’s fully separate from a third (an "All" chained into a "No"), the nested category and the separate one can never overlap in any diagram — ruling out any possibility conclusion that requires them to.
Worked examples
1. 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.
Solution
- 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.
Answer: Both possibilities are valid
2. 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.
Solution
- 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.
- 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.
Answer: Only possibility I is valid
3. 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.
Solution
- 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."
Answer: Neither possibility is valid
4. 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.
Solution
- 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."
- But pens outside that book-overlap aren’t constrained at all — some of them could be tables, making "some pens are tables" possible.
Answer: Only possibility II is valid
Try these yourself
Check whether each possibility can be drawn in at least one valid diagram, then check against the answer.
1. 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.
Answer: Only possibility I is valid
2. 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.
Answer: Both possibilities are valid
3. 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.
Answer: Only possibility I is valid
Where this comes up
Syllogism: Possibility Cases is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — building on the standard Syllogism lesson.
Practice more Syllogism: Possibility Cases questions
This page covers the approach and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Syllogism: Possibility Cases (and every other Reasoning/Quant/English topic) with instant scoring and explanations — free, no account required.
Practice Syllogism Possibility Cases free →