Statements and conclusions, Venn diagrams
Logical Reasoning - Draw valid conclusions from statements
Statement 1 (Major Premise): All A are B
Statement 2 (Minor Premise): All B are C
Conclusion: All A are C ✓
| Type | Statement | Venn Diagram |
|---|---|---|
| A (Universal Affirmative) | All A are B | A inside B |
| E (Universal Negative) | No A is B | A and B don't overlap |
| I (Particular Affirmative) | Some A are B | A and B overlap |
| O (Particular Negative) | Some A are not B | Part of A outside B |
┌─────────────────┐
│ B │
│ ┌─────┐ │
│ │ A │ │
│ └─────┘ │
└─────────────────┘
A is completely inside B
┌─────────┐
│ A │
│ ┌──┼──────┐
│ │ │ B │
└──────┼──┘ │
└─────────┘
A and B overlap
┌─────────┐ ┌─────────┐
│ A │ │ B │
└─────────┘ └─────────┘
Completely separate
All A are B
All B are C
∴ All A are C ✓
All A are B
Some B are C
∴ Some A may be C (not definite!)
No A is B
All C are A
∴ No C is B ✓
✗ "All A are B" does NOT mean "All B are A"
Example: All dogs are animals ≠ All animals are dogs
✗ "Some A are B" does NOT mean "Some A are not B"
(They might all be B!)
✗ "Some A are not B" does NOT mean "Some A are B"
When neither conclusion follows individually,
check if EITHER...OR follows together.
Statement: Some A are B. All B are C.
Conclusion I: All A are C (Not definite)
Conclusion II: Some A are not C (Not definite)
But "Either I or II" might be valid if one must be true.
| If Given | You Can Conclude |
|---|---|
| All A are B | Some B are A |
| Some A are B | Some B are A |
| No A is B | No B is A |
| Some A are not B | Nothing about B and A |
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