Syllogism – Reasoning Ability
(Maharashtra Police Constable – Reasoning Ability – Study Notes)
1. Simple Explanation
A syllogism is a short logical argument that contains two premises (statements) and a conclusion.
- Premise 1: Statement about a relation between two groups.
- Premise 2: Another statement about one of those groups.
- Conclusion: Logical inference that must follow from the two premises.
Example
- All cats are mammals.
- All mammals are warm‑blooded.
→ Conclusion: All cats are warm‑blooded.
The conclusion must be true if the premises are true.
2. Types of Syllogisms
| # | Pattern | Example | Condition for Validity |
|---|---|---|---|
| 1 | All A are B. All B are C. → All A are C | All roses are flowers. All flowers are plants → All roses are plants | “All” → universal affirmative |
| 2 | No A is B. All B are C. → No A is C | No dog is a cat. All cats are pets → No dog is a pet | “No” → universal negative |
| 3 | All A are B. No B is C. → No A is C | All sparrows are birds. No bird is a mammal → No sparrow is a mammal | “All” + “No” |
| 4 | No A is B. No B is C. → No A is C | No fish is a bird. No bird is a mammal → No fish is a mammal | “No” + “No” |
| 5 | Some A are B. Some B are C. → Some A are C | Some men are tall. Some tall people are athletes → Some men are athletes | “Some” → particular affirmative |
| 6 | All A are B. Some B are C. → Some A are C | All painters are artists. Some artists are musicians → Some painters are musicians | One universal + one particular |
| 7 | Some A are B. No B is C. → No A is C | Some birds are penguins. No penguin is a flight‑capable bird → No bird is flight‑capable | Particular + universal negative |
| 8 | No A is B. Some B are C. → No A is C? | No tiger is a cat. Some cats are predators → Not Determined | Cannot be concluded – need more info |
Rule of Thumb – If a statement has “All” or “No”, it is universal. If it has “Some”, it is particular.
3. Key Points for Solving Syllogisms
| # | Strategy | What to Look For |
|---|---|---|
| 1 | Identify the subject and predicate | Words at the start and end of each clause |
| 2 | Determine the quantity | “All”, “No”, “Some” |
| 3 | Match patterns | Use the table above to find the correct deduction |
| 4 | Check for contradictions | If the conclusion contradicts a premise, it’s invalid |
| 5 | Use a logic tree | Write the premises vertically and the conclusion at the bottom |
| 6 | Avoid false assumptions | Do not assume the existence of a group when not stated |
| 7 | Multiple conclusions | Some syllogisms allow more than one correct conclusion; choose the most specific |
| 8 | Practice with time | Set a timer (1–2 minutes) for each question to improve speed |
4. Worked Example
Premise 1: All students are humans.
Premise 2: All humans are mortal.
Conclusion:
- All students are mortal.
(Use Pattern 1: All A are B + All B are C → All A are C.)
Step‑by‑Step
| Step | Action | Reason |
|---|---|---|
| 1 | Identify A, B, C | A = students, B = humans, C = mortal |
| 2 | Check quantities | Both premises use “All” → universal |
| 3 | Apply pattern | Pattern 1 → All A are C |
| 4 | State conclusion | All students are mortal |
5. Practice Question
Premise 1: No lizard is a mammal.
Premise 2: All mammals are warm‑blooded.
Which of the following is a valid conclusion?
a) No lizard is warm‑blooded.
b) All lizards are warm‑blooded.
c) Some lizards are warm‑blooded.
d) No warm‑blooded animal is a lizard.
Solution
-
Identify groups
- A = lizard
- B = mammal
- C = warm‑blooded
-
Quantities