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Chapter 8
- Immediate Inference - Transformation & Equivalence
- You can transform A E I O statements in various ways.
We will look at transforming a statement into its converse, obverse, or contrapositive.
| Statement | (A,E,I, or O) |
| Converse | - Swap terms
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| Obverse | - A<->E or I<->O
- Complement of 2nd term
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| Contrapositive | - Swap terms
- Complements of both terms
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Let's look at transformations for each of the statement types.
| For an A Statement | A: All M are P |
| Converse | A: All P are M |
| Obverse | E: No M are non-P |
| Contrapositive | A: All non-P are non-M |
| For an E Statement | E: No X are Z |
| Converse | E: No Z are X |
| Obverse | A: All X are non-Z |
| Contrapositive | E: No non-Z are non-X |
| For an I Statement | I: Some S are B |
| Converse | I: Some B are S |
| Obverse | O: Some S are not non-B |
| Contrapositive | I: Some non-B are non-S |
| For an O Statement | O: Some L are not C |
| Converse | O: Some C are not L |
| Obverse | I: Some L are non-C |
| Contrapositive | O: Some non-C are not non-L |
- There is a table that tells you whether a statement is equivalent to its converse, obverse, or contrapositive.
| A: | E: | I: | O: |
| Is the Converse equivalent? | NO | YES | YES | NO |
| Is the Obverse equivalent? | YES | YES | YES | YES |
| Is the Contrapositive equivalent? | YES | NO | NO | YES |
- Kelley calls this Immediate Inference, since the truth of a statement allows you to immediately infer the truth of equivalent statements.
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