An Introduction to
Answers to Exercises 29
Formal Logic
A
Use QL trees to evaluate the entailment claims (1) to (10) in Exercises 28A.
x(Fx Gx) f x(Gx Fx)
1.
x(Fx Gx)
x(Gx Fx)
x(Gx Fx)
(Ga Fa)
Ga
Fa
(Fa Ga)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Fa
(8)
(9)
Ga
The tr
An Introduction to
Formal Logic
A
Answers to Exercises 35
Use QL= trees to show the following inferences are valid:
1.
Jack (m) is Fingers (n). Fingers is never caught (F). Whoever is never caught (F) escapes justice (G). So Jack escapes justice.
(1)
(2)
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MTH215 Symbolic Logic
13 Dec 2014
Week 10 Assignment
MTH215 Symbolic Logic
Brandon Johnson
13 Dec 2014
Page 218
A
a.1
Suppose m denotes Socrates, n denotes Plato, o denotes Aristotle, Fx means x is a
philosopher, Gx means x is wise, Mxy me
Brandon Johnson
MTH215 Symbolic Logic
31 Oct 2014
Week 4 Assignment
MTH215 Symbolic Logic
Brandon Johnson
31 Oct 2014
B. The strict negations of the sentences on the left can be expressed as on the right:
1. No one loves Jack
3. Everyone who loves Jack ad
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07 Dec
2014
MTH215 Symbolic Logic
Week 6 Assignment
MTH215 Symbolic Logic
Brandon Johnson
07 Dec 2014
Page 209
We are to translate QL expressions into natural English, using the following
interpretation:
The domain of discourse is people
m
Week 5 -Mid Term Examination Model
Central Penn College
Math 215 Symbolic Logic
Brandon Johnson
Indicate the premises and conclusions of the following arguments. Which of these
arguments do you suppose involve deductively valid reasoning? Why?
1. It will
Brandon Johnson
MTH215 Symbolic Logic
15 Nov 2014
Week 6 Assignment
MTH215 Symbolic Logic
Brandon Johnson
15 Nov 2014
Page 81
B. Suppose P means Fred is a fool; Q means Fred knows some logic; R means Fred is a
rocket scientist. Then the best we can do by
Answers to Exercises 8
A
Show the following expressions are wffs by producing construction trees for them. Which is the
main connective of each wff? Also, list all the subformulae of the last two examples.
1.
2.
3.
4.
5.
6.
(P P) R)
(R S) Q)
(P Q) (P Q)
(
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MTH215 Symbolic Logic
16 Oct 2014
Week 2 Assignment
MTH215 Symbolic Logic
Brandon Johnson
16 Oct 2014
Chapter 3 Review Questions
Part A
Some F are G; no G is H; so, some F are not H.
Valid (those Fs which are G are not H).
1.
3. All F are
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MTH215 Symbolic Logic
11 Oct 2014
Week 1 Assignment
MTH215 Symbolic Logic
Brandon Johnson
11 Oct 2014
Page 8 Review Questions
2. Most politician are corrupt. After all, most people are corrupt and politicians are ordinary
people.
Premisses
Answers to Exercises 32
Question
In addition to the properties of relations already dened, we say that a relation R is Euclidean just if,
whenever a has R to b, and a has R to c, then b has R to c. R is asymmetric if, whenever a has R to b, then
b does no
An Introduction to
Formal Logic
Answers to Exercises 27
Take the following q-valuation
The domain is cfw_Romeo, Juliet, Benedick, Beatrice
Constants are assigned references as follows:
m Romeo
n Juliet
Predicates are assigned extensions as follows:
F cfw
An Introduction to
Formal Logic
Answers to Exercises 34
Yet more Welsh affairs! Using the same translation manual as 34.3 i.e.
a means Angharad
b means Bryn
m means Mrs Jones
F means speaks Welsh
G means is a girl
L means loves
M means is taller than
an
Answers to Exercises 33
A
More Welsh affairs! Using the same translation manual as 33.2, translate the following into QL=:
1.
Angharad and Mrs Jones are one and the same.
a=m
2.
At least one Welsh speaker loves Bryn.
x(Fx Lxb)
(Remember: at most one needs
Answers to Exercises 25
A
Show the following simple arguments are valid by translating into QL and using trees.
1.
Everyone is rational; hence Socrates is rational.
Translation: x Fx Fn Here and throughout well assume the domain is people. And of
course t
An Introduction to
Formal Logic
Answers to Exercises 26
Which of the following are wffs of QL? Which are sentences, i.e. closed wffs? In the open wffs, which
occurrences of which variables are free? What is the main logical operator of each wff?
1
zy( Myz
Answers to Exercises 24
A
Suppose m denotes Myfanwy, n denotes Ninian, o denotes Olwen, Fx means x is a philosopher,
Gx means x speaks Welsh, Lxy means x loves y, and Rxyz means that x is a child of y and z. Take
the domain of discourse to consist of huma
Answers to Exercises 11
A
Give truth-tables for the following wffs (i.e. calculate the value of the wff for every assignment of values to the atoms: you can, however, use short-cuts).
1.(P P)
2. (P (P Q)
3.(R Q) P)
4.(P Q) R)
5.(P Q) (P Q)
6.(P Q) (R (P Q
Answers to Exercises 17
A
Use the tree test to determine which of the following arguments (from Exercises 13A) are tautologically valid:
1.
(P Q) P
(P Q)
P
P
Q
The tree closes, so the inference is tautologically valid. Note you should have ticked off the
Answers to Exercises 23
A
Suppose m denotes Socrates, n denotes Plato, o denotes Aristotle, Fx means x is a philosopher,
Gx means x is wise, Mxy means x taught y. Take the domain of discourse to consists of people.
And then translate the following into QL
Answers to Exercises 22
We are to translate QL expressions into natural English, using the following interpretation:
The domain of discourse is people
m stands for Socrates
n stands for Plato
F means is wise,
G means is a philosopher
L means loves ,
We wi
Answers to Exercises 14
A
Given
P expresses Plato is a philosopher
Q expresses Quine is a philosopher
R expresses Russell is a philosopher
S expresses Socrates is a philosopher
translate the following into PLC as best you can:
1.
2.
3.
4.
5.
6.
7.
8.
9.
1
Answers to Exercises 10
Insert quotation marks into the following where necessary to make them accord to the customary conventions and come out true.
1
means much the same as and
means much the same as and
2
P can be interpreted as meaning that grass i
Answers to Exercises 16
1. We start assuming that the premisses and the negation of the conclusion are all true:
(R P) T
(R Q) T
(P Q) T
(1)
(2)
(3)
A negated disjunction is true (i.e. the disjunction is false) if each disjunct is false, i.e.
(4)
(5)
P T
Answers to Exercises 9
A
We are given that P means Plato is a great philosopher; Q means Quine is a great philosopher; R
means Russell is a great philosopher. With that manual, the translations go into PL as follows:
1.
Either Quine is a great philosopher
!
!
!
!
Answers to Exercises 13
A
Use the truth-table test to determine which of the following arguments are tautologically valid:
1.
(P Q)
P
P
T
T
F
F
Q
T
F
T
F
(P Q)
F
F
P
F
F
T
T
We evaluate the conclusion rst, and then ignore lines 3 and 4 which are a
Answers to Exercises 5
Which of the following arguments are valid? Where an argument is valid, provide a proof. Some
of the examples are enthymemes that need repair.
1. No philosopher is illogical. Jones keeps making argumentative blunders. No logical per
Answers to Exercises 1
Indicate the premisses and conclusions of the following arguments. Which of these arguments
do you suppose involve deductively valid reasoning? Why?
1
Whoever works hard at logic does well. Accordingly, if Russell works hard at logi