1. EDUCTION

2. Eduction
An immediate inference that involves the reformulation of a given proposition by the interchange of the subject and the predicate of a given proposition or the use or removal of the negatives.
Kinds of Formal Eduction
1. Obversion
2. Conversion
3. Contraposition
4. Inversion

3. Obversion Rules of Obversion Examples
Retain the subject and the quantity of the obvertend
Change the quality: if the obvertend is affirmative change to negative; if negative change to affirmative
Contradict the predicate
Examples
1. A – E Every man is trustworthy. No man is untrustworthy
2. E – A No man is indispensable. Every man is dispensable.
3. I – O Some creatures are lucky. Some creatures are not unlucky.
4. O – I Not all commodities are expensive. Some commodities are inexpensive.
1. His lecture is not without humor. So, it must have humor.
2. All soldiers are combatants. Hence, no soldiers are noncombatants.

4. Obversion Truth-value of the obverse
To determine the truth-value of the obverse, always remember that the obvertend and the obverse are logically equivalent, that is, they have the same truth value.
Note:
Obvertend the given proposition
Obverse the new proposition
Obversion the process itself.

5. Conversion
Derives the inference by interchanging the subject and the predicate.
There are two types of conversion:
Simple Conversion: E and I
Limited Conversion: A and E
O does not have a conversion
Notes
Convertend the given proposition
Converse the new proposition
Conversion the process itself

6. Conversion Rules of Conversion
Interchange the subject and the predicate.
Retain the quality of the proposition.
Do not extend the term, that is, a particular term cannot be universal term
2 Kinds of Conversion: Simple Conversion and Limited Conversion
Examples of Simple Conversion
1. E – E No flowers are fruits. No fruits are flowers.
2. I – I Some animals are mammals. Some mammals are animals.

7. Conversion Examples of Limited Conversion Truth-value of the converse
A – I All men are mortal. Some mortal (beings) are men.
E – O No aliens are voters. Some voters are not aliens.
Truth-value of the converse
Simple converses are logically equivalent to their convertends
Limited converses have their truth value determined through the law of subalternation. Thus
If the convertend is true, the converse is true.
If the converse is false, the converse is doubtful.

8. Contraposition
The formulation of a new proposition whose subject is the contradictory of the original predicate
There are two types of contraposition:
Partial Contraposition
Full or complete contraposition
I does not have a contraposition
Notes
Contraponend the given proposition
Contraposit the new proposition
Contraposition the process itself

9. Contraposition Rules of Partial Contraposition Examples
The subject is the contradictory of the original predicate.
Change the quality.
The predicate is the original subject.
Examples
1. A – E Every man is trustworthy. No untrustworthy (person) is a man.
2. E –I No dogs are cats. Some non-cats are dogs.
3. O – I Not all citizens are voters. Some non-voters are citizens.

10. Contraposition Rules of Full Contraposition Examples
The subject is the contradictory of the original predicate.
The quality is the same.
The predicate is contradictory of the original subject.
Examples
1. A – A Every man is trustworthy. Every untrustworthy (person) is a non-man.
2. E – O No dogs are cats. Some non-cats are not non-dogs.
3. O – Not all citizens are voters. Some non-voters are not non-citizens.

11. Inversion
The formulation of a new proposition whose subject is the contradictory of the original subject
There are two types of Inversion:
Partial Inversion
Full or complete Inversion
I and O do not have a inversion
Note
Invertend the given proposition
Inverse the new proposition
Inversion the process itself

12. Inversion Rules of Partial Inversion Examples
The subject is the contradictory of the original predicate.
Change the quality.
The predicate is the original subject.
Truth value follows the laws of subalternation.
Note: O and I have no inversion
Examples
1. A – O Every man is trustworthy. Not every non-man is trustworthy.
2. E – I No dogs are cats. Some non-dogs are cats

13. Inversion Rules of Full Contraposition Examples
The subject is the contradictory of the original subject.
The quality is the same.
The predicate is contradictory of the original predicate.
Examples
1. A – I Every man is trustworthy. Some non-man are untrustworthy.
2. E – O No dogs are cats. Some nondogs are not noncats.
Truth-Value
Inversions follow the laws of subalternation. Thus
If the invertend is true, the inverse is true.
If the inverted is false, the inverse is doubtful.