Appendix
1.
Rules of Inference
1.
3.
5.
Modus Ponens (M.P.)
2.
Modus Tollens (M.T.)
pq
pq
p
q
q
p
(H.S.)
4.
(D.S.)
pq
pq
qr
p
p r
q
(C.D.)
6.
Absorption (Abs.)
(p q) (r s)
pq
pr
p (p q)
q s
7.
Simplification (Simp.)
8.
Conjunction (Conj.)
pq
p
p
q
LOGIC Spring 2015
Exercise 12
Section: _
A. For each of the following proofs state the Rule of Inference by which its
conclusion follows from its premises.
Proof No.1
Proof No.2
1. (x)(Px~Mx) Asmp.
1. (x)(Px~Qx)
2. (x)(SxMx) Asmp /(x)(Sx~Px)
2. (x)(PxRx)
LOGIC Spring 2015
Exercise 09
Section _
Rewrite the following syllogistic arguments into premise-conclusion structure and
check their validity by using Venn diagrams.
(1) All CD players are expensive and delicate mechanisms, but no expensive and
delicate
LOGIC Spring 2015
Exercise 08
Section _
A. For each of the following argument state the Rule of Inference by which its
conclusion follows from its premises.
Proof 1:
Proof 2:
1. ZA
Asmp.
1. WX
Asmp.
2. Z v A
Asmp. / A
2. YX
Asmp. / (W v Y) X
3. ~A ~Z
_
3.
LOGIC Spring 2015
Exercise 05
For the following paragraphs:
(a) rewrite the argument in premise(s)-conclusion structure:
(b) extract the argument form by using the symbolic notations;
(c) check the validity of the argument form by using the truth table te
LOGIC Spring 2015
Exercise 10
Translate the following syllogistic arguments into standard form, and test their
validity by using Venn diagrams.
(1) Some nondrinkers are athletes, because no drinkers are persons in perfect physical
condition, and some peop
LOGIC Spring 2015
Exercise 11
Section: _
A. Given that S exists and All S are P is true, determine whether the following
propositions are true, false or undetermined:
1. No S is P.
2. Some S are P.
3. Some S are not P.
4. All non-P are non-S.
5. No non-P
LOGIC Spring 2015
Exercise 07
A. For each of the following argument state the Rule of Inference by which its
conclusion follows from its premises.
Proof 1:
Proof 2:
1.
AB
Asmp.
1.
(~M ~N) (ON)
Asmp.
2.
A v (C D) Asmp.
2.
NM
Asmp.
3.
~B~E
Asmp. / C
3.
~M
A
LOGIC Spring 2015
Exercise 06
A. Construct a truth-table for each formula and state whether the formula is
tautologous, contradictory, or contingent.
(01) ( p ~q ) ( q p )
(02) ( (p q) r ) ( ~r ( p q ) )
B. Change the following argument into premises-conc
LOGIC Spring 2015
Exercise 04
For the following paragraphs:
(a) rewrite the argument in premise(s)-conclusion structure;
(b) extract the argument form by using the symbolic notations;
(c) check the validity of the argument form by using the truth table te
Identity, Numerals and Definite Descriptions
A. Interpretation of the Symbol of Identity, numerals and definite descriptions
1. Identity and Its Negation
Peter is equal to David
a=b
Peter is not equal to David a b
2. Exceptive
Except Peter, all students u
LOGIC Spring 2015
Exercise 01
Try to rewrite the following arguments in premises-conclusion structure:
1. If a bear is hungry, it is not a friendly animal. Therefore, no friendly animals are
hungry bear.
2. Some women are queens. No queens are poor. So, s
Key to Exercise 12
A. For each of the following proofs state the Rule of Inference by which its
conclusion follows from its premises.
Proof No.1
1. (x)(Px~Mx)
2. (x)(SxMx)
3. Py~My
4. SyMy
5. ~My~Sy
6. Py~Sy
7. ~(~Sy)~Py
8. Sy~Py
9. (x)(Sx~Px)
Proof No.2
LOGIC Spring 2015
Exercise 03
I.
Fill in the truth values:
p
q
T
T
T
F
F
T
F
F
~p
(pq)
(pq)
(p v q)
(~p ~q)
~(p v ~q)
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II.
Rewrite the following sentences by using the basic truth functi
Key to Exercise 10
Translate the following syllogistic arguments into standard form, and test their
validity by using Venn diagrams.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(1) Some nondrinkers are athletes, because no drinker
Key to Exercise 11
A. Given that S exists and All S are P is true, determine whether the following
propositions are true, false or undetermined:
1. No S is P.
2. Some S are P.
3. Some S are not P.
4. All non-P are non-S.
5. No non-P is S.
6. Some P are no
LOGIC Spring 2015
Exercise 02
1. Can an argument have all true premises and a true conclusion and yet not be
deductively valid?
2. Can a deductively valid argument have false premises?
3. Can a deductively valid argument have a false conclusion?
4. Can a
Key to Exercise 09
Rewrite the following syllogistic arguments into premise-conclusion structure and
check their validity by using Venn diagrams.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(1) All CD players are expensive and de
Key to Exercise 05
For the following paragraphs:
(a) rewrite the argument in premise(s)-conclusion structure;
(b) extract the argument form by using the symbolic notations;
(c) check the validity of the argument form by using the truth table techniques.
x
Key to Exercise 06
A. Construct a truth-table for each formula and state whether the formula is
tautologous, contradictory, or contingent.
(01) ( p ~q ) ( q p )
p
q
( p ~q ) ( q p )
T
T
T T FT T T T T
T
F
T T TF T F T T
F
T
F F FT T T F F
F
F
F T TF T F T
Key to Exercise 04
For the following paragraphs:
(a) rewrite the argument in standard format;
(b) extract the argument form by using the symbolic notations;
(c) test the validity of the argument form by using the truth table techniques.
xxxxxxxxxxxxxxxxxx
Key to Exercises 08
A. For each of the following argument state the Rule of Inference by which its
conclusion follows from its premises.
Proof 1:
Proof 2:
1. ZA
Asmp.
1. WX
Asmp.
2. Z v A
Asmp. / A
2. YX
Asmp. / (W v Y) X
3. ~A ~Z
1 Trans.
3. ~W v X
4. ~(
Key to Exercise 01
Try to rewrite the following arguments in premises-conclusion structure:
1. If a bear is hungry, it is not a friendly animal. Therefore, No friendly animals are
hungry bear.
The Argument:
If a bear is hungry, it is not a friendly animal
Key to Exercise 02
1. Can an argument have all true premises and a true conclusion and yet not be
deductively valid? ( Yes )
2. Can a deductively valid argument have false premises? ( Yes )
3. Can a deductively valid argument have a false conclusion? ( Ye
Key to Exercise 07
A. For each of the following argument state the Rule of Inference by which its
conclusion follows from its premises.
Proof 1:
Proof 2:
1.
AB
Asmp.
1.
(~M ~N) (ON)
Asmp.
2.
A v (C D) Asmp.
2.
NM
Asmp.
3.
~B~E
Asmp. / C
3.
~M
Asmp. / ~O
4
Key to Exercise 06
I.
Fill in the truth values:
p
q
~p
(pq)
(pq)
(p v q)
(~p ~q)
~ (p v ~q)
~p q
T
T
FT
TTT
TTT
TTT
FT T FT
F T T FT
F FT
T
F
FT
TFF
TFF
TTF
FT T TF
F T T TF
F FF
F
T
TF
FTT
FFT
FTT
TF F FT
T F F FT
T TT
F
F
TF
FTF
FFF
FFF
TF T TF
F F T TF
Extended arguments
In daily life, we usually encounter
extended arguments such as those found
in newspapers.
Our task is to sort out the arguments and
organize them in the simple form of a
flowchart.
1
Methods
1. Use numerals to label various
statement