1. VENN DIAGRAMS AND
CATEGORICAL PROPOSITION

2. 1. An empty circle is used to
represent a subject class or a
predicate class and is generally so
labeled with an S or a P. Putting
the name of the actual subject or
predicate class next to the circle is
preferred.

3. 2. Shading or many parallel lines
are used to indicate areas which are
known to be empty. I.e., there are
no individuals existing in that area.
E.g., the diagram to the right
represents the class of "Yeti."

4. 3. The third symbol used is an "X"
which represents "at least one" or
"some" individual exists in the area
in which it is placed. The diagram
to the right indicates "some thing."

5. Venn Diagrams in General
1.Universal affirmative proposition
1. The A form, "All S is P," is
shown in the diagram to the right.
Notice that all of the S's are pushed
out, so to speak, into the P class. If
S's exist, they must be inside the P
circle since the left-hand lune of
the diagram is shaded and so is
empty.

6. 2. Universal negative proposition
2. The E form, "No S is P," is
shown in the diagram to the
right. Notice that the lens area
of the diagram is shaded and so
no individual can exist in this
area. The lens area is where S
and P are in common; hence,
"No S is P." All S, if there are
any, are in the left-hand lune,
and all P, if there are any, are
relegated to the right-hand lune.

7. 3. The I form, "Some S is P," is
much more easily seen. The "X" in
the lens, as shown in the diagram to
the right, indicates at least one
individual in the S class is also in
the P class.

8. 4. The O form, "Some S is not P,"
is also easily drawn. The S that is
not a P is marked with an "X" in
the S-lune. This area is not within
the P circle and so is not a P. It is
worth while to note, that from this
diagram we cannot conclude that
"Some S is P" because there is no
"X" in the lens area. Thus, studying
this diagram will explain why
"Some S is not P" does not entail
"Some S is P."

9. SYMBOLIC LOGIC

10. SYMBOLS
Symbols comprise every language. Per se,
symbols are effective tools of human
activities whether in social interaction or
in the search for knowledge.

11. This part will help us understand Symbolic Logic, its
basic components and structures, symbols and fucntions
of statements constituting a basic argument.
This process of proving validity is an indispensable tool to
recognize the universal patters of valid arguments.

12. Truth-Functional Operators
Four types of truth-functional compounds,
1. Conjunctions (Conjunctive Proposition)
Here are some words that in many standards uses yield
conjunctions;
_____and_______
Both____and________
______but_______
______yet_______
______although_______
______whereas________
______while________

13. Manuel is strong and Gina is pretty.
Both Manuel is strong and Gina is pretty.
Manuel is strong but Gina is pretty.
Manuel is strong yet Gina is pretty.
Manuel is strong although Gina is pretty.
Manuel is strong whereas Gina is pretty.
Manuel is strong while Gina is pretty.

14. 2. Disjunction (Disjunctive Proposition)
Here are some words that in many of their standard use yield
disjunctions.
Either_____or_______
______or_______
______unless_______
Either Manuel is strong or Gina is pretty.
Manuel is strong or Gina is pretty.
Manuel is strong unless Gina is pretty.

15. 3. Implication (Conditional Proposition)
If ____then______
If____, _____
_____only if_____
_____if______
_____provided that______
not____unless_______
If Manuel is strong then Gina is pretty.
If Manuel is strong, Gina is pretty.
Manuel is strong only if Gina is pretty.
Gina is pretty if Manuel is strong.
Gina is pretty provided that Manuel is strong.
Manuel is not strong unless Gina is pretty.

16. 4. Material Equivalence (Bi-Conditional Proposition)
Here are some phrases that in many of their standard uses yield
material equialence:
_______if, and only if,_______
_______when, and only when,______
_______is equivalent to _______
These phrases can result into material equivalences, such as:
Manuel is strong if, and only if, Gina is pretty.
Manuel is strong when, and only when Gina is pretty.
Manuel is strong is equivalent to Gina is pretty.

17. Negation (Contradictory or denial)
It is not the case that______
It is not true that_______
There is no way that________
______is false.
It is false that_______
It is not the case that Manuel is strong.
It is not true that Manuel is strong.
There is no way that Manuel is strong.
“Manuel is strong” is false.
It is false that Manuel is strong.

18. End