Syllogism • Topic 2 of 4

Venn Method for Syllogism

The diagram method removes all guesswork. Draw circles to satisfy the statements in the most general way, then test the conclusion: if you can draw even one legal diagram where it fails, reject it.

The 3-step method

  1. Draw the universals first. "All" and "No" fix the layout — they leave no freedom.
  2. Add the "Some" overlaps in the most general way — keep circles as separate as the statement allows, so you don't accidentally create links that weren't given.
  3. Test the conclusion against the picture. Then deliberately try to redraw it to BREAK the conclusion. If you can't, it follows; if you can, it doesn't.

Worked example — why two "Somes" prove nothing

Statements: Some A are B. Some B are C. Conclusion: Some A are C?

A B C A overlaps B, B overlaps C — but A and C need not meet
A legal diagram where A and C never touch ⇒ "Some A are C" does NOT follow.

Both "Some" statements are satisfied (A meets B, B meets C), yet A and C are completely apart. Because we found one legal diagram that breaks it, the conclusion fails.

The #1 mistake. Drawing only the diagram where everything overlaps, then "seeing" a conclusion that isn't forced. Always try to pull the circles apart.

Contrast — a chain that DOES follow

All A are B. No B is C. Conclusion: No A is C. Since A sits entirely inside B, and B is wholly separate from C, A cannot reach C in any diagram — so it follows.

✅ Solved examples

1. Some A are B. Some B are C. Conclusion: Some A are C?
You can draw A–B overlap and B–C overlap with A and C disjoint. So it does NOT follow.
2. All A are B. Some B are C. Conclusion: Some A are C?
C may overlap only the part of B outside A. Does NOT follow.
3. No A is B. Some B are C. Conclusion: Some C are not A?
Those B that are C are not A, so some C are not A. Follows.
4. All A are B. No B is C. Conclusion: No A is C?
A is inside B, B is apart from C, so A is apart from C. Follows.

✏️ Practice — try these, take hints as needed

1. Some A are B. All B are C. Some A are C?
The A∩B are C.
—
—
Follows
2. Some A are B. Some B are C. Some A are C?
Try to separate A and C.
—
—
Does not follow
3. All A are B. No C is B. No A is C?
A inside B, C apart from B.
—
—
Follows
4. No A is B. No B is C. No A is C?
A and C could still overlap.
—
—
Does not follow
5. All A are B. All A are C. Some B are C?
A is common to B and C.
—
—
Follows

📝 Topic test — 8 questions

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