1. An argument is (deductively) valid if:
a. Whenever the premises are true, necessarily, the conclusion is true.
b. The premises are actually true and the conclusion is true.
c. There is a possible situation in which the premises are true and the conclus
Exercise 1. Which of the below list the symbols that can be in a wff:
1. P, Q, R, S, , , , &
2. P, Q, R, S, T,0 , (, ), , ,
3. P, Q, R, S,0 , (, ), , ,
Exercise 2. Translations.
R= The circle is red.
Q= The triangle is purple.
P= The circle is purple.
S
Exercise 1. Translations.
R= The circle is red.
P= The circle is purple.
Given the above translate these sentences:
a. The circle is red, if it is not purple.
(P R)
b. If the circle isnt purple, then it is red.
(P R)
c. The circle isnt purple only if its
Exercise 1. Translations.
R= The circle is red.
P= The circle is purple.
Given the above translate these sentences:
a. The circle is red, if it is not purple.
b. If the circle isnt purple, then it is red.
c. The circle isnt purple only if its red.
d. The
Exercise 1. If there are n atomic sub-formulas how many rows are there in the truth table?
Exercise 2. Connect these words to there definitions:
Tautology
The name for our formalisation of if and only if (sometime write iff).
Bi-conditional
In the truth t
A leaf or foot node is a node in a tree with no other nodes under it.
Exercise 1. Label the following on the tree: a) the root node, b) a fork, c) two leaf/foot nodes, d) a
path in the tree.
(P (Q R)
Node (Root)
P
Node
Q
Node
Fork
P
(Q R)
Node (Leaf/Foot)
1. An argument is (deductively) valid if:
a. Whenever the premises are true, necessarily, the conclusion is true.
b. The premises are actually true and the conclusion is true.
c. There is a possible situation in which the premises are true and the conclus
Overview of the Method of Truth Trees
Rules for Trees
Remember to write the results of applying a rule under every open path containing
the wff being analyzed.
Non-branching Rules
(A B)X
AX
A
(A B)X
(A B)X
A
B
A
B
A
B
Branching Rules
(A B)X
(A B)X
(A B)X
Exercise 1. If there are n atomic sub-formulas how many rows are there in the truth table?
2n
Exercise 2. Connect these words to there definitions:
Tautology
The name for our formalisation of if and only if (sometime write iff).
Bi-conditional
In the trut
First Midterm Exam
LPS/Phil 30Spring 2016
1. Formalize the English statements below in PLC, using the atomic wffs P , Q, R, and
S, interpreted according to the following translation manual:
P : Penny will go to the party.
Q: Leonard will go to the party.
LPS/Philos 30 Homework 3 Solutions
Greg Lauro
May 5, 2016
NB: Depending on the order in which you applied the rules, your trees
may be different then the ones presented here. However, if the tree is open,
you will find your truth-value assignment among th
LPS/Philos 30 Homework 2 Solutions
Greg Lauro
April 20, 2016
1. (a) Neither.
P ( P ( P P )
T
T T T T F T
F
F F F T T F
(b) Neither.
P Q (
T T
T F
F T
F F
T
F
T
T
Q
T
F
T
F
(c) Tautology.
Q S (
T T
T F
F T
F F
Q
T
T
F
F
( P Q )
F T T T
F T T F
F F T T
T F
LPS/Philos 30 Homework 1 Solutions
Greg Lauro
April 15, 2016
1. (a) (P Q)
(b) (Q S)
(c) (R S)
(d) (P Q), or equivalently (P Q)
(e) (Q S)
(f) (P S)
(g) (P Q) (P Q), or equivalently (P Q) (P Q)
2. (a) Construction tree:
P
P
P
P
P
(P P )
P
(P P ) P )
Main co
A leaf or foot node is a node in a tree with no other nodes under it.
Exercise 1. Label the following on the tree: a) the root node, b) a fork, c) two leaf/foot nodes, d) a
path in the tree.
(P (Q R)
P
Q
P
(Q R)
Q
R
Exercise 2. When is a path open? When i