Testing the validity of logical conclusions from two given statements, using Venn diagrams to check every possible case.
📖 ~14 min read🧩 SSC Reasoning
Introduction
Syllogism gives two statements about categories (using "All," "Some," or "No") and asks which conclusions
logically must follow. The most reliable method is drawing every possible Venn
diagram consistent with the statements and checking if the conclusion holds in all of them.
Four Basic Statement Types
Statement
Venn Diagram Meaning
All A are B
A circle is completely inside B circle
No A is B
A and B circles are completely separate, no overlap
Some A are B
A and B circles overlap partially (at least one common element)
Some A are not B
Part of A circle lies outside B circle
Diagram — "All A are B" vs "No A is B" vs "Some A are B"
The Complementary Pair Rule — Key Shortcut
💡 High-Yield Rule: If two conclusions form a complementary pair — such as "All A are B" and "Some A are not B," or "Some X are Y" and "No X is Y" — then at least one of the two conclusions must always be true ("either...or" case), even if neither is individually certain.
Q. Statements: All cats are dogs. All dogs are birds. Conclusions: I. All cats are birds. II. Some birds are cats.
Draw: Cat circle inside Dog circle, Dog circle inside Bird circle → Cat is fully inside Bird too
I. All cats are birds — follows (direct chain containment)
II. Some birds are cats — follows (since all cats, a non-empty set, are within birds, some birds must be cats) Both conclusions follow.
Q. Statements: Some pens are books. Some books are tables. Conclusion: Some pens are tables.
"Some-Some" statements can be drawn in multiple valid ways — the overlapping "books" region shared by pens and tables need NOT be the same subset
Draw at least one valid diagram where pens and tables circles do NOT intersect at all (only both separately overlap books)
Since a valid diagram exists where the conclusion is false, the conclusion does not follow.
Possibility-Based Conclusions
Some questions ask "Is it possible that..." rather than "Does it definitely follow" — for these, you only need to find one valid diagram where the statement could be true (not check all diagrams).
✅ Practice Focus: Four basic statement-to-diagram mappings · "Some-Some" statements rarely yield definite conclusions (test with a non-overlapping diagram) · Complementary pair rule for "either...or" answers · Possibility vs definite-conclusion question distinction.