Icse Syllogism
Data Sufficiency — Icse Syllogism
Icse Syllogism
Syllogisms — Logical Deduction
What is a Syllogism?
A syllogism is a logical argument with:
- Two or more premises (given statements assumed to be true)
- A conclusion derived from those premises
The task: decide if the conclusion necessarily follows from the premises — regardless of real-world truth.
Even if the premises are absurd ("All cats are fish"), you must treat them as true and check if the conclusion follows logically.
Venn Diagram Method (Most Reliable)
Draw circles to represent the sets in the statements, then check if the conclusion is always/never/sometimes true.
Types of Statements:
| Statement | Meaning | Venn Representation |
|---|---|---|
| All A are B | A ⊆ B (A is inside B) | Small circle A inside large circle B |
| No A are B | A ∩ B = ∅ | Two separate circles |
| Some A are B | A ∩ B ≠ ∅ | Two overlapping circles |
| Some A are not B | Part of A is outside B | A overlapping B, part of A outside |
Standard Conclusion Patterns
| Premises | Valid Conclusion |
|---|---|
| All A are B. All B are C. | All A are C. |
| All A are B. No B are C. | No A are C. |
| Some A are B. All B are C. | Some A are C. |
| All A are B. Some B are C. | Some A are C. — NOT valid (some B that are C may not be A) |
| No A are B. All B are C. | Some C are not A. |
Worked Examples
Example 1:
Premises: All mangoes are fruits. All fruits are sweet. Conclusion: All mangoes are sweet. Valid ✓ (All A→B, All B→C: All A→C)
Example 2:
Premises: All dogs are animals. Some animals are wild. Conclusion: Some dogs are wild. Invalid ✗ — The wild animals might be the non-dog animals. Draw Venn: dogs (A) inside animals (B); some overlap of B with C (wild) — could be entirely outside A.
Example 3:
Premises: No pen is a pencil. All pencils are stationery. Conclusion: Some stationery is not a pen. Valid ✓ — The pencils are stationery and are not pens → some stationery is not a pen.
Common Traps
- Real-world knowledge vs logic: "All elephants are small" is false in real life, but if given as a premise, treat it as true.
- "Some" does not mean "many" — "some" means "at least one."
- Reversed conclusion: "All A are B" does NOT mean "All B are A."
- Complementary pairs: If conclusion I is true, check if conclusion II is its complement.
Strategy for ICSE Questions
- Draw Venn diagrams for both premises
- Check if conclusion is always true (in all possible Venn configurations)
- For "either-or" questions: if neither I nor II follows but together they cover all cases → "Either I or II follows"
- Answer choices: (A) Only I, (B) Only II, (C) Both, (D) Neither, (E) Either I or II
Quick Practice
- All roses are flowers. No flower is a tree. Conclusion: No rose is a tree. (True/False?)
- Some boys are smart. All smart people are successful. Conclusion: Some boys are successful. (True/False?)
- No cat is a dog. All dogs are mammals. Conclusion: Some mammals are not cats. (True/False?)
- All A are B. Some C are B. Conclusion: Some C are A. (True/False?)
- Stretch: If "Some students are toppers" and "All toppers are hard workers", what can you definitely conclude about students and hard workers?
Key Takeaways (TL;DR)
- What is a Syllogism?
- Venn Diagram Method (Most Reliable)
- Standard Conclusion Patterns
- Worked Examples
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