PHIL 102 Introductory Logic
Fall 2023
Problem Set #11
30 points possible
Due: 11/10 by 11:59 PM CST, submitted as a PDF on Blackboard.
Instructions: Answer all parts of each question to get full credit. Students are encouraged to
collaborate with their peers, but each must write up and hand in their own assignments.
Group Study Sessions: Group study sessions, held by the Success TA Ryan Kim, are held
virtually on Tuesdays and on campus on Mondays, Thursdays, and Fridays. They’re designed to
be a resource for everyone to work together on problem sets. But you should particularly
consider attending if you are finding the material difficult. For information about how to attend,
see the course Blackboard site.
Question 1. Construct proofs to show the following claims are true. Make sure to include a citation
for each line you add to the proof. 4 points each
a) ¬ B → G ⊢ ¬ G → B
BETTS
#
u
!
i
,
76
7/ I
DE 2-4
3
S
2
-E 1
G
-
reductio
6
7
25
B
S
7
97
R
R
G
716-8
TG
10
-B
->
[2 4
-
b) ¬ (D ∧ E) ⊢ D → ¬ E
#IDE)
2
3
4
+D
TE
I↑
S
-
NEI
D
D
E
Iz
6
714
-
6
el1
7
,
Question 2. Construct proofs to demonstrate each of the following claims. 4 points each
¬ (P ∧ ¬ Q) is provably equivalent to P → Q
The sentences ¬ (B ∨ C), A → B, and ¬A → B are provably inconsistent.
Continued on the next page
Question 3. Translate the following sentences from FOL to English, using the translation key
provided. 3 points each
g = gold
n = nitrogen
o = oxygen
p = plutonium
l = lead
Txyz = ___x is between ___y and
___z on the periodic table
Fx = ___x is flammable
Hxy = ___x is heavier than ___y
Mx = ___x is a metal
Vxy = ___x is more valuable than ___y
Sxy = ___x is on the same row of the periodic
table as ___y
a) ¬ (Fn → Mn)
Its not the
a
case
that if
nitrogen
is
flammable then
,
nitrogen
metal
b) (Ml ∧ Mg) ∧ Slg
Lead
and
periodic
Gold
table
are
as
metals
Gold
,
and lead
is
on
the
same
row
of
.
Question 4. Translate the following sentences from English to FOL, using the same translation
key as for Question 3. 4 points each
a) Either lead is not a metal, or lead is between oxygen and plutonium on the periodic table.
7 MI rTlop
is
b) Lead is heavier than gold, but gold is more valuable than lead.