8.22 Quick Revision -- Syllogism

Four Statement Types

Type	Statement	Example
A	All A are B	Universal Affirmative
E	No A is B	Universal Negative
I	Some A are B	Particular Affirmative
O	Some A are not B	Particular Negative

Venn Diagram Quick Reference

  All A are B:       No A is B:        Some A are B:      Some A are not B:
  +-------+          +---+ +---+       +--+--+--+         +------+--+---+
  |   B   |          | A | | B |       | A|XX| B|         |  A   |XX| B |
  | +---+ |          +---+ +---+       +--+--+--+         +------+--+---+
  | | A | |
  | +---+ |
  +-------+

Chain Rules (MEMORIZE!)

P1	P2	Conclusion
All A-B	All B-C	All A are C
All A-B	No B-C	No A is C
Some A-B	All B-C	Some A are C
Some A-B	No B-C	Some A are not C
Some + Some	--	NO definite conclusion
Negative + Negative	--	NO definite conclusion
Some-not + anything	--	Usually NO conclusion

Conversion Rules

Original	Converts To
All A are B	Some B are A
No A is B	No B is A
Some A are B	Some B are A
Some A are not B	NO valid conversion

Complementary Pairs (Either-Or)

  Pair 1: "Some A are B" (I) <---> "No A is B" (E)
  Pair 2: "All A are B"  (A) <---> "Some A are not B" (O)

If neither conclusion of a pair follows alone, then "Either...or..." follows.

Possibility Questions

• Possibility is TRUE if ANY valid diagram supports it
• Possibility is FALSE only if it contradicts ALL diagrams
• If a conclusion is definite, its possibility is automatically TRUE

Key Rules

1. Middle term must be distributed in at least one premise
2. Two negatives = no conclusion
3. Two particulars = no conclusion
4. One negative premise -> conclusion must be negative
5. "All A are B" does NOT mean "All B are A"

Exam Strategy (~50 sec/question)

1. Read and classify premises (A/E/I/O) - 10 sec
2. Draw Venn diagram(s) - 15 sec
3. Test conclusions - 15 sec
4. Check Either-Or if needed - 10 sec

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