Syllogism
Why This Chapter Matters
Syllogism has 5-10 marks in every Banking exam. The new pattern includes possibility cases which confuse many candidates. Master the rules and you can score full marks.
Core Concepts
1. Basic Statements (Propositions)
Universal Affirmative (A): "All A are B"
Universal Negative (E): "No A is B"
Particular Affirmative (I): "Some A are B"
Particular Negative (O): "Some A are not B"
2. Venn Diagram Approach
Draw circles representing each category. Check which arrangement(s) satisfy ALL given statements.
Conclusion is valid if it's TRUE in ALL possible Venn diagrams (not just one).
3. Rules for Direct Conclusions
| Premise 1 | Premise 2 | Valid Conclusion |
|---|
|---|---|---|
| All A are B | All B are C | All A are C |
|---|---|---|
| All A are B | No B is C | No A is C |
| Some A are B | All B are C | Some A are C |
| Some A are B | No B is C | Some A are not C |
| All A are B | Some B are C | Some A are C (may not always follow — check Venn) |
Quick rule: Universal + Universal → can give Universal or Particular
Particular + Particular → NO definite conclusion
4. Possibility Cases (New Pattern — Most Tricky!)
Statement: "Some A are B"
Possibility: "All A are B" is POSSIBLE (because "Some A are B" doesn't say anything about the rest of A)
Not possible: "No A is B" (contradicts the statement)
Statement: "No A is B"
Possibility: "Some A are not B" is POSSIBLE (in fact, it definitely follows)
Not possible: "Some A are B" or "All A are B"
Statement: "All A are B"
"Some A are B" is DEFINITELY TRUE (a consequence)
"All B are A" is POSSIBLE (if circles overlap perfectly) but not definite
Key rule for possibility:
"All/Some A are B is possible" = the circles for A and B CAN overlap (even if not stated they do)
"No A is B is possible" = the circles CAN be separate
5. Common Mistakes
"Some A are B" does NOT mean "Some A are not B" (the rest of A might also be B)
"All A are B" DOES imply "Some A are B" (true if A is non-empty)
"No A is B" DOES imply "Some A are not B"
Practice Problems
Q1: Statements: All cats are dogs. Some dogs are rats.
Conclusions: (I) Some cats are rats (II) Some rats are cats.
I: Not definite (some dogs are cats, some dogs are rats, but they may not overlap)
II: Same issue. Neither follows definitely. Answer: Neither follows.
Q2: Statements: No book is pen. All pens are bags.
Conclusions: (I) No book is bag (II) Some bags are not books.
Possible Venn: Books outside {pen,bag}. Pens inside bags.
I: Not necessary (bags could include non-pen items that might overlap with books). Actually: No pen is a book (from no book is pen, symmetric). Bags include pens, may include other things. Books may or may not be bags. I does NOT definitely follow.
II: Pens are bags. No pen is book. So pens (which are bags) are not books → Some bags are not books. II FOLLOWS.
Q3 (Possibility): Statements: Some apples are oranges.
Conclusion: All apples are oranges is a possibility.
True — "some" doesn't rule out "all". Possibility is valid.
Previous Year Questions
IBPS PO 2023: 4-statement syllogisms with 2 conclusions + 2 possibility cases.
SBI Clerk 2022: New pattern with coded syllogisms (symbols replace words).