Syllogism: Reasoning Ability Notes for Andaman & Nicobar Islands PSC

Reasoning Ability – Syllogism

Andaman & Nicobar Islands PSC – Study Notes

1️⃣ What is a Syllogism?

A syllogism is a form of logical reasoning that involves two premises (statements that are assumed to be true) and a conclusion that follows necessarily from those premises.
In PSC exams, syllogisms are used to test deductive reasoning, inference, and the ability to draw valid conclusions from given facts.

Example
Premise‑1: All mammals are warm‑blooded.
Premise‑2: All dogs are mammals.
Conclusion: All dogs are warm‑blooded.

The conclusion follows logically from the premises.

2️⃣ Key Elements of a Syllogism

Element	Description	Example
Premises	Two statements that are accepted as true.	“All birds can fly.” “Penguins are birds.”
Conclusion	Statement that necessarily follows from the premises.	“Penguins can fly.” (But here it’s false – a classic logical trap!)
Terms	Words that appear in the premises and conclusion.	All, Some, No
Quantifiers	Express the quantity of the subject.	All, Some, No
Subject & Predicate	In “All X are Y”, X is the subject, Y the predicate.	X = birds, Y = animals

3️⃣ Types of Syllogisms (Common in PSC)

Type	Pattern	Example
All‑All	All A are B. All B are C. → All A are C.	All A are B. All B are C. → All A are C.
All‑Some	All A are B. Some B are C. → Some A are C.	All students are humans. Some humans are artists. → Some students are artists.
All‑No	All A are B. No B are C. → No A are C.	All mammals are warm‑blooded. No warm‑blooded animals are cold‑blooded. → No mammals are cold‑blooded.
Some‑All	Some A are B. All B are C. → Some A are C.	Some cats are pets. All pets are domesticated. → Some cats are domesticated.
Some‑Some	Some A are B. Some B are C. → Some A are C.	Some flowers are red. Some red things are roses. → Some flowers are roses.
Some‑No	Some A are B. No B are C. → No A are C.	Some fruits are sweet. No sweet things are bitter. → No fruits are bitter.

Tip: Remember the “All‑All” rule – if both premises are “All”, the conclusion will also be “All”.

4️⃣ How to Solve a Syllogism

Identify the Premises
- Read each statement carefully.
- Highlight the subject, predicate, and quantifier.
Determine the Relationship
- Check if the relationship is All, Some, or No.
- Note if the premises share a common term (the “bridge” term).
Apply the Rule of Inference
- Use the type table to decide the quantifier of the conclusion.
- Ensure the conclusion’s subject and predicate are correctly mapped.
Check for Validity
- Test the conclusion with a real‑world example to see if it always follows.
- Avoid “All A are B” + “All B are C” → All A are C (valid), but All A are B + All B are C → All A are C (valid only if B is a subset of C; otherwise, it may be false).
Answer Quickly
- PSCs often give 5‑10 syllogisms per question.
- Focus on the pattern; you don’t need to write a full sentence.

5️⃣ Worked Example

Premise‑1: All artists are creative.
Premise‑2: Some creative people are musicians.
Conclusion?

Step	Action	Reason
1	Identify quantifiers	Premise‑1 = All, Premise‑2 = Some
2	Identify the bridge term	“Creative”
3	Determine conclusion type	All‑Some → Some
4	Derive conclusion	Some artists are musicians.
5	Check validity	True: Some artists (who are creative) can be musicians.

Answer: Some artists are musicians.

6️⃣ Common Pitfalls & How to Avoid Them

Pitfall	Why it Happens	Fix
Confusing “All” with “Some”	Misreading the quantifier.	Highlight or underline the quantifier.
Missing the Bridge Term	Overlooking the common term.	Write the bridge term in the margin.
Assuming “No A are B” + “All B are C” → “No A are C”	Misapplied inference.	Remember that “No” in the first premise makes the conclusion No only if the second premise is All.
Using Real‑World Logic Instead of Formal Logic	Overthinking “truth” of statements.	Stick to the logical structure, not the factual accuracy.
Not Checking All Cases	Skipping the “Some” possibility.	Verify if the conclusion could be All, Some, or No.

7️⃣ Quick Revision Summary

Topic	Key Point
Definition	Deductive reasoning with two premises → conclusion.
Terms	Premise, conclusion, subject, predicate, quantifier, bridge term.
Quantifiers	All, Some, No.
**Inference