Syllogism • Topic 3 of 4

Possibility Cases

Some conclusions are phrased as possibilities ('Some A can be C', 'All B being C is a possibility'). A possibility follows if you can draw at least ONE legal diagram in which it is true — the opposite test from definite conclusions.

Definite vs possible — opposite tests

Type of conclusionIt is accepted when…Your job
Definite ("Some A are C")it holds in every diagramhunt for a diagram that BREAKS it
Possibility ("All A can be C")it holds in at least one diagramhunt for a diagram that MAKES it true
Flip your strategy. For a definite conclusion you try to refute; for a possibility you try to confirm. Mixing these two up is the most common error in this topic.

Example

Statement: Some A are B. Is "All A are B" possible?

B A A drawn fully inside B
Drawing A entirely inside B still satisfies "Some A are B" ⇒ "All A are B" is possible.

Because we can legally draw A inside B (which still makes "some A are B" true), the possibility holds. By contrast, if the statement were "No A is B", then "Some A are B" is impossible — that statement forbids any overlap.

✅ Solved examples

1. Some A are B. Possibility: All A are B?
Draw A fully inside B — consistent with "some". So the possibility holds.
2. All A are B. Possibility: Some B are not A?
B can be larger than A, leaving some B outside A. Possibility holds.
3. No A is B. Possibility: Some A are B?
"No A is B" forbids any overlap — the possibility cannot hold.
4. Some A are B. Possibility: No A is B?
"Some A are B" guarantees an overlap, so "no A is B" is impossible.

✏️ Practice — try these, take hints as needed

1. Some A are B. Possibility: All B are A?
Draw B inside A.
—
—
Holds
2. All A are B. Possibility: All B are A?
Let the circles coincide.
—
—
Holds
3. No A is B. Possibility: All A are B?
Overlap is forbidden.
—
—
Does not hold
4. All A are B. Possibility: Some A are not B?
All A are inside B.
—
—
Does not hold
5. Some A are not B. Possibility: All A are B?
Some A are outside B.
—
—
Does not hold

📝 Topic test — 8 questions

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