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
(
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)
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Week 10 Assignment
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Page 218
A
a.1
Suppose m denotes Socrates, n denotes Plato, o denotes Aristotle,
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Week 4 Assignment
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B. The strict negations of the sentences on the left can be expressed as on the ri
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MTH215 Symbolic Logic
Week 6 Assignment
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Page 209
We are to translate QL expressions into natural English, using the follow
Week 5 -Mid Term Examination Model
Central Penn College
Math 215 Symbolic Logic
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Indicate the premises and conclusions of the following arguments. Which of these
arguments do you suppos
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Week 6 Assignment
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Page 81
B. Suppose P means Fred is a fool; Q means Fred knows some logic; R means
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 exam
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Week 2 Assignment
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Chapter 3 Review Questions
Part A
Some F are G; no G is H; so, some F are not H.
V
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Week 1 Assignment
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Page 8 Review Questions
2. Most politician are corrupt. After all, most people are
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
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 Juli
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 me
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 spe
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 throu
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? W
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
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
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 ta
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 consi
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
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
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 sam
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
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 int
!
!
!
!
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 co
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. Jo
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 logi