Syllogism: Reasoning Ability Notes for Manipur Police Sub-Inspector (SI)

Syllogism – Reasoning Ability (Manipur Police SI Exam)

Syllogism is a deductive argument that consists of three parts:
Premise 1 + Premise 2 ➜ Conclusion

The goal is to decide whether the conclusion necessarily follows from the premises.

Term	Meaning	Example
Premise	A statement assumed to be true.	1) All birds have wings. 2) A sparrow is a bird.
Conclusion	The statement that is inferred from the premises.	Therefore, a sparrow has wings.
Valid Syllogism	Conclusion must be true if premises are true.	The above example is valid.
Invalid Syllogism	Conclusion can be false even if premises are true.	Premise 1: All cats are animals. Premise 2: All dogs are animals. Conclusion: All cats are dogs. (False)

Key Idea:
If the premises are true, and the syllogism is logically valid, the conclusion cannot be false.

#	Concept	What to Look For	Why It Matters
1	Two- premise structure	Always 2 premises → 1 conclusion	Nothing else is needed.
2	Categorical Syllogism	Uses All/No/Some statements (A, E, I, O).	Most exam syllogisms.
3	Syllogistic Forms (Aristotelian)	15 valid patterns (e.g., Barbara, Celarent, Darii, Darien).	Memorizing a few common ones speeds solving.
4	Mood & Figure	Mood = type of each proposition (A/E/I/O). Figure = position of the middle term.	Helps identify the pattern quickly.
5	Middle Term	Appears in both premises but not in the conclusion.	Must be distributed in at least one premise for validity.
6	Distribution Rules	If a term is distributed in the conclusion, it must be distributed in at least one premise.	Prevents hidden assumptions.
7	Negation & Contraposition	Some syllogisms allow dropping or negating terms.	Useful for “negative” conclusions.
8	Common Pitfalls	① Premises are true but conclusion is false (invalid). ② Wrong placement of “not”. ③ Forgetting distribution rules.	Avoids wrong answers.
9	Speed Tips	① Identify the middle term quickly. ② Match the mood/figure. ③ Use “mood-figure” tables.	Saves time during the test.
10	Examples of Valid Forms	Barbara (AAA‑1): All A are B. All B are C. → All A are C.	Classic example.

Figure	Middle Term Position	Example Mood	Valid?
1	Premise 1: M‑B, Premise 2: B‑C	A A I	✅
2	Premise 1: B‑M, Premise 2: M‑C	A I A	✅
3	Premise 1: M‑B, Premise 2: C‑M	I A A	✅
4	Premise 1: B‑M, Premise 2: C‑M	A A I	✅
5	Premise 1: M‑B, Premise 2: M‑C	E I A	✅ (e.g., Darien)

(Only the most common valid patterns are listed; for exam use, memorize the 4–5 patterns that appear most frequently.)

Statement

Premise 1: All students are learners.
Premise 2: All teachers are students.
Conclusion: All teachers are learners.

Identify Terms
- A = teachers
- B = students
- C = learners
Check Premises
- Premise 1: All B are C → A (All B are C)
- Premise 2: All A are B → A (All A are B)
Determine Mood & Figure
- Mood: A A A
- Figure: Middle term B is subject in Premise 1 and predicate in Premise 2 → Figure 1.
Match to Valid Form
- AAA‑1 is the classic Barbara syllogism → valid.
Conclusion
- Since the syllogism matches a valid pattern, the conclusion is necessarily true.

Result: Valid syllogism → Correct answer: Yes, the conclusion follows.

Premise 1: All cats are animals.
Premise 2: All dogs are animals.
Conclusion: All cats are dogs.