Feb 12th

To determine immediate inference, look at whether the inference is apparent. Ex: No As
are Bs, No Bs are As

There are no other possible interpretations, therefore the conversion is valid (remember
that conversions of E statements are valid an
Feb 27th, 12:00 PM
More examples from section 6.3
p. 348 Use truth tables to determine whether the following symbolized statements are
Tautologous, selfcontradictory, or contingent
I1. N ( N N)
N
T
F
(N N)
T
T
N ( N N)
T
T
This is a tautology because all
Feb 13th
Chapter 5: Categorical Syllogisms

Syllogism is a deductive argument consisting of two premises and one conclusion.
The Major term is the predicate of the conclusion statement. It is usually a general rule,
an axiom.
 The Minor term is the subj
Feb 20th, 12:00 PM
Rules of Syllogistic logic (and their fallacies)
1. The middle term of a syllogism must be distributed at least once
a. There must be some existence of connection between the major and minor terms
b. If the middle term is not distribute
No I are P
All T are P
Some T are not I

EAO 2
Can immediately infer that it is invalid to Boole because again it concludes a particular
from a universal proposition
This argument is conditionally valid
All C are P
All C are T
Some T are P

AAI 3
For
Feb 18th, 12:00 PM
Another example of diagramming categorical syllogisms with Venn diagrams
No F are T
All F are C
Some C are not T


EAO 3 argument
Automatically we can say that this is invalid from the Boolean standpoint because a
particular proposit
Feb 16th, 12:00 PM
Diagramming categorical syllogisms with Venn diagrams

When diagramming these syllogisms, always start with the universal premise rather than
the particular
 When diagraming the particular proposition, only focus on the two classes to
Converse
Truth Value
Fallacy
Converse
A
All P are S
Fallacy of Illicit conversion
O
Some P are not S
I
E
Some P are S
No P are S
Undetermine
d
Undetermine
d
Same
Same
Obverse
A
O
I
E
No S are non P
Some S are non P
Some S are non P
All S are non P
Same
Sa
Feb 11th
The quiz this coming Friday will cover all of Chapter 4 (4.1 4.7)
Brief review of Boolean square of opposition:

The only relationships which can be drawn given no other information than the
truthfulness/falsity of a particular statement is its
Feb 23rd, 12:00 PM
The quiz this Friday will be on the sections 5.1 5.3 and 6.1 6.3
_
Chapter 6: Propositional logic

The units are whole statements (propositions)
Simple statements are represented by capital letters (A,B,C, etc.)
These are combined via
Mar 11th, 12:00 PM
Section 6.6: Argument Forms and Fallacies of Propositional Logic

Many arguments in propositional logic have forms that can be immediately identified as
valid or invalid.
Also note these arguments may not be true, but as long as there
Classifications of individual compound statements:
 Tautologous: where truth values under the main operator are all true (the rightmost
column)
 Selfcontradictory: where truth values under the main operator are all false
 Contingent: there is at leas
Mar 9th, 12:00 PM
Proving validity of arguments with truth tables (cont.)
 There are two methods to proving whether a propositional argument is valid or invalid
 One may set up the entire truth table for the argument considering all possible truth value
Feb 25th, 12:00 PM
Section 6.2: Truth tables
A
T
F
A truth table allows one to evaluate arguments by showing every possible case how the
truth value of a compound statement is determined by the truth values of its parts
~A
F
T
The truth table for negation
II2. For these exercises fill in the missing premise and justify the conclusion
1. ~A
2. A v E
3. _
4. ~A E
The premise is E, derived by 1, 2, DS
Given conclusion is given by 1, 3, Conj
III4. Use the first 8 rules of inference to derive the conclusion of
Brief intro to Section 7.1: Natural Deduction in Propositional Logic

Natural Deduction is a stepbystep method for proving the validity of propositional type
arguments
It shows exactly how the conclusion comes out of the premises
1. A B
2. ~A ( C v D)
Mar 13th, 12:00
The Exam next Wednesday will cover sections 5.1 5.3, All of Chapter 6, and the parts of
Chapter 7 covered up to and including Monday
_
Section 7.2: Further rules of Implication

Like with the previous argumentative forms, it is very impor
p. 355 Use indirect truth tables to determine the validity of these arguments
II1.
K ~ K
K

K ~ K
F
K
F
Here, there is only one premise. However, the argument is still valid because there we
have been unable to show that assuming the conclusion is false
April 24th, 12:00
Section 8.6: Relational Predicates
 Continued from last class, there are overlapping statements, where the quantifiers overlap
each other
 Examples: (x)(y) Dxy would translate to Everything is different from something
o (x)(y) translat
April 22nd, 12:00
Further example in Section 8.5
p. 494
II4.
Given:
1. (x) (Ax Bx)
2. (x) Ax
(x) (Bx)

A a Ba
F
Aa
T
Ba
F
It is impossible to show that this argument is invalid in a universe with one object.
Therefore a universe of two objects must be a
Given:
Note that the final reason for the proof (3 7, CP) can be given next to the conclusion
while the conclusion is not stated on the final line of the proof (this is also optional)
Again note ACP is the given reason for assuming A and the conditional
Mar 20th, 12:00
Reviewing problems from the test
Directions: Use either the direct or indirect methods to show that an argument is valid or invalid
in propositional logic. First, state whether the argument is valid or invalid. Second, state which
valid or
Mar 23rd, 12:00
Reviewing problems from the test (cont.)
Given:
Derive: ~(~F v G) ([~ A A) ( B B)]
1. [(A A) ( B B)]
2. (A B) ( C v D)
3. D (~ F ~G)
4. ~C
5. (A B)
1, Taut
6. (C v D)
2.5. MP
7. ~C D
6, Impl
8. D
4, 7, MP
9. ~(F ~G)
3,8, MP
10. (A B) (~ F
Mar 27th, 12:00
There was a quiz today on section 7.1 7.6, so the notes are fairly short today.
_
Brief Intro to Section 8.1: Predicate Logic
 Simply put, predicate logic is a combination of categorical and propositional logic
 The most basic terms of p
Mar 25th, 12:00
More conditional proof: p. 442: Derive the following argument using conditional proof
Given:
Derive: (E H) J (4 12, CP)
1. E ( F G)
2. H ( G I)
3. (F I) ( J v ~H)
4. E H
ACP
5. E
4, Simp
6. (F G)
1, 5, MP
7. H E
4, Comm
8. H
7, Simp
9. (
Mar 30th, 12:00

Section 8.1: Predicate Logic
Last class covered the universal quantifier, x, y, or z.
There is also the Particular quantifier, or the Existential quantifier
x( Hx Lx) means there exists at least one human that is living
x( Hx ~Lx) means
Mar 16th, 12:00
As noted before, the exam will cover 5.1 5.3, all of Chapter 6, and 7.1 7.4
_
Section 7.4: More Rules of Replacement
 Again rote memorization can only be achieved by doing several homework problems
from the text.
 One should be familiar
Directions:. The following arguments are valid. Apply the argument forms and rules to prove
the validity of the following arguments.
_
Given:
Derive: [A (B v C)] ~ C
1. [A (B v C)] ( A D)
2. (A D) ( A v ~C)
3. ~A
4. (A B) v (A C)
5. [A (B v C)]
6. (A D)
April 1st, 12:00
More practice in Section 8.2
p. 473
I2.
Given:
1. (x) (Bx Cx)
2. (x) (Ax Bx)
3. An Bn
4. An
5. Bn An
6. Bn
7. Bn Cn
8. Cn
9. (Ax Cx)

Derive: (x) (Ax Cx)
2, EI
3, Simp
3, Comm
5, Simp
1, UI
7, Simp
4, 8, Conj
Note that the reasoning for