The document discusses different types of propositional logic operations including conversion, obversion, and contraposition. It defines each operation, provides examples of how to apply the rules to different proposition forms like A, E, I, and O propositions, and illustrates the steps to derive the converse, obverse, or contrapositive of a given proposition.

1. Opposition of propositions may be illustrated in the ff. diagram for clearer comprehension:
A / Every dog
A E / No dog is
E/ No dog is
CONTRARY
Everyanimal
is an dog is an animal
an animal
S S
U U
B B
A A
L CONTRADICTORY
L
T T
E E
R R
N N
I / Some dogs O /Some dogs
O/ Some dogs
SUBCONTRARY
are animals
are animals are not animals
are not animals

2. Eduction
 1. Conversion. the formulation of a new proposition
by interchanging the subject with the predicate of the
original proposition without changing the quality. The
original proposition is called “convertend” and the
newly formulated proposition is called “converse”.
 Example: (observe closely the quantity and quality)
 Convertend: All men are not females.
 Converse: All females are not men.
 Take note that the quality is not altered in the
converse. Both convertend and converse are negative.

3. Eduction
 There are two (2) types of conversion: the Simple and
the Partial.
 a) Simple conversion. One whose convertend and
converse have the same quantity. If the convertend is
universal then the converse is also universal. If it is
particular the converse is also particular.
 Convertible under Simple Conversion are E
propositions and I propositions.
 E – E : No man is a dog.
 No dog is a man.

4. Egypt
 We call our dog EGYPT.
 He always leaves a pyramid in every room

5. Eduction
 There are 2 propositions that cannot be converted
under simple conversion. They are the A and O. “All
men are mortal cannot be converted to “All mortals are
men.”
 An O proposition like “Some flowers are not roses.”
cannot be converted simply as follows: “Some roses
are not flowers.”
 Give examples of
E–E Both combinations can be converted
I–I simply

6. Partial Conversion
b) Partial conversion. The quantity of the convertend
is reduced from universal to particular. A is partially
converted to I; E is partially converted to O.
Examples:
A to I: All roses are flowers All trees are plants
Some flowers are roses Some plants are trees
E to O: No human being is a monkey
Some monkeys are not human beings.

7. Rules of conversion
1. Interchange the subject and predicate.
2. Retain the quality.
3. In simple conversion, retain the quantity.
4. In partial conversion, reduce the quantity from
universal to particular.
5. There is no simple conversion for A proposition.

8. Eduction
 2. Obversion. The process of reformulating a new
proposition by maintaining the subject and quantity of
the proposition but changing its quality and then
replace the predicate with its contradictory. The
original proposition is called “obvertend” and the new
proposition “obverse”, and the process is called
“obversion”.
 example:
Every apple is a plant
Every apple is not a non-plant or No apple is not a
non-plant

9. Rules of Obversion
The following are the rules in obverting propositions:
1. Retain the subject-term and quantity iof the
obvertend.
2. Change the quality. If the obvertend is affirmative, the
obverse is negative and vice-versa
3. Put the predicate in its contradictory.
Under Rules 1 and 2 the ff. are obvertible:
A to E
E to A
I to O
O to I

10. Examples of Obversion
A to E: All women are beautiful
All women are not non-beautiful or
No women are non-beautiful
E to A: Every Cordilleran is not Japanese
Every Cordilleran is a non-Japanese
I to O: Some people are Filipinos
Some people are not non-Filipinos.
O to I: Some students are not brown
Some students are non-brown.
You will note that the obvertend and the obverse have the same meaning.

11. Same Meaning
CHEATING . . . is two wrong people doing the right
thing.
Can I pray while smoking? Or
Can I smoke while praying?

12. Eduction
 3. Contraposition. The formulation of a new proposition by
undergoing the process of obversion and conversion.The
original proposition is called “contraponend” and the new
propositon is called “contraposit”, and the process
contraposition. There are two (2) types of contraposition,
the partial and the complete. For our purposes let go
immediately to the complete contraposition.
There are three (3) steps to follow:
1. First obvert the contraponend.
2. Then, convert the obverse.
3. Then, obvert the converse to get the contraposit.
In other words the 3 steps are: obvert, convert, obvert

13. Complete contraposition/ examples
By complete contraposition the ff. can be contraposed:
A to A, E to O and O to O.
Examples:
A to A: Every creature is finite.
(obvert) Every creature is not non-finite.
(convert) Every non-finite is not a creature.
(obvert) Every non-finite is a non-creature.

14. Complete contraposition/ examples
E to O: A cat is not a tree.
(obvert) A cat is a non-tree.
(convert) Some non-tree are cats.
(obvert) Some non-trees are not non-cats.
O to O: Some citizens are not voters.
(obvert) Some citizens are non-voters.
(convert) Some non-voters are citizens.
(obvert) Some non-voters are not non-citizens.