Syllogism: Reasoning Ability Notes for FCI Recruitment

📚 Syllogism – Study Notes for FCI Recruitment (Reasoning Ability)

Syllogism is a form of deductive reasoning that uses two premises to reach a conclusion.
It is the backbone of many reasoning questions in the FCI Recruitment exam.

1️⃣ Simple Explanation

Term	Meaning
Major Premise	General statement that contains the major term (usually the predicate of the conclusion).
Minor Premise	Specific statement that contains the minor term (usually the subject of the conclusion).
Conclusion	Deductive statement that follows from the two premises.
Major Term	The predicate of the conclusion.
Minor Term	The subject of the conclusion.
Middle Term	Appears in both premises but not in the conclusion; it connects the major and minor terms.

Structure (in words):
Major Premise : All A are B.
Minor Premise : All C are A.
Conclusion : All C are B.

2️⃣ Key Points (Quick Reference)

#	Concept	What to remember
1	Categorical Syllogism	Involves all or no statements; uses terms A, E, I, O.
2	Three Figures	Placement of the middle term: 1st figure (middle = major), 2nd figure (middle = minor), 3rd figure (middle = middle).
3	Three Moods	Combination of major, minor, and conclusion types: e.g., AAA (All‑All‑All).
4	Validity Rules	1. Middle term used once in each premise. 2. Middle term is not the exclusive subject. 3. If a premise is negative, conclusion must be negative. 4. A negative premise cannot have a positive conclusion.
5	Common Fallacies	Illicit major/minor, exclusive middle, undistributed middle, affirming the consequent, converse error.
6	Hypothetical & Disjunctive Syllogisms	Used in “if‑then” or “either‑or” patterns.
7	Relevance to FCI	Questions often test the ability to identify the correct form, check for fallacies, and derive the conclusion.

3️⃣ Worked Example

Question (Typical FCI style)

All managers are dedicated.
Some employees are not dedicated.
Which of the following is a valid conclusion?
a) Some employees are not managers.
b) No manager is an employee.
c) All employees are managers.
d) Some managers are not employees.

Step‑by‑Step Solution

Identify terms
- Major Term (predicate of conclusion): manager
- Minor Term (subject of conclusion): employee
- Middle Term: dedicated
Classify premises
- Premise 1: “All managers are dedicated” → Universal affirmative (A).
- Premise 2: “Some employees are not dedicated” → Particular negative (O).
Check validity rules
- Rule 3 (If a premise is negative, conclusion must be negative).
- Rule 2 (The middle term must be distributed in at least one premise).
- Rule 1 (Middle term appears in both premises).

Form the syllogism

Major: All M are D (A)
Minor: Some E are not D (O)
Conclusion?  (must be negative)

Possible conclusions in negative form
- Some E are not M (O).
- No M are E (E).
Check each option
- a) Some employees are not managers → O (fits).
- b) No manager is an employee → E (fits).
- c) All employees are managers → A (contradicts rule 3).
- d) Some managers are not employees → O (but violates rule 1? Actually the conclusion is fine; however, we need to see if it's derivable given premises).
Derive the valid conclusion
Using the standard O–A form (Major A, Minor O, Conclusion O) → Option a is valid.

Answer: a) Some employees are not managers.

4️⃣ Quick Revision Summary

Topic	Take‑away
Definition	Syllogism = two premises → one conclusion.
Structure	Major, Minor, Conclusion (terms: major, minor, middle).
Rules of Validity	1. Middle used once in each premise. 2. Middle is not the exclusive subject. 3. Negative premise → negative conclusion.
Common Fallacies	Illicit major/minor, undistributed middle, exclusive middle, affirming the consequent.
Categorical Forms (Mood & Figure)	AAA, EAE, etc. Remember the 3 figures (placement of middle term).
Practical Tip	Before solving, write the premises in A, E, I, O format; then check the conclusion against the rules.
FCI Focus	Look for the type of syllogism (categorical, hypothetical), ensure distribution of terms, and watch for negatives.

Pro Tip:
Always start by identifying the major, minor, and middle terms in the given statements.
Then, classify each premise as A, E, I, or O.
Apply the validity rules; if any rule is broken, the conclusion is invalid.

Good luck with your FCI