B. Valid or invalid? Use the truth-assignment method to determine.
Logic PHIL 2001 Elisabeta Sarca -----TEST XXXXXXXXXXName__________________________________________________________
Student Number____________________________________________
1. Peonies are neither fragrant nor delicate, provided they
are plastic.
2. To understand the material, it’s not sufficient to attend
class.
3. You’ll reap the rewards of your work only if you have
some luck and you persevere.
4. Flattering your teacher is neither necessary nor sufficient
for getting a good grade.
5. Cats don’t cuddle unless they feel content and trust the
person.
6. A necessary condition for my ma
ying you is that you buy
me a Buick.
1. (T ⊃ (Y • S))
Y
T
2. ((B• ~Z) v ~(~N v F))
(~K • F)
~(K v ~B)
3.((H • F) ⊃ R)
~R
~F
4. ~((Q v ~P) • ~W)
~(Q ⊃ ~A)
((A • ~C) • W)
1. Either you are lean and mean, or you are fluffy and jolly.
Since you aren’t mean, you must be jolly.
2. To get to either London or Cardiff, you must take the
train. You didn’t get to Cardiff, but you got to London. So,
you must have taken the train.
C. Translate into propositional logic and say whether valid or invalid.
2 points each x 6 = 12 points A. Translate into propositional wffs.
4 points each x 4 = 16 points
6 points each x 2 = 12 points
ATTENTION: All responses (where applicable) should show clear evidence of the work through which you reached
the answer. You may use the last page as scrap. Do not forget to write your name on the test!
T =
Y =
S =
B =
Z =
N =
F =
K =
H =
F =
R =
Q =
P =
W =
A =
C =
1. Unless the weather is inclement the match will take
place, but our team will surely never give up.
2. Acing biology 101 is not a necessary condition for
qualifying for medical school.
1. That Luna takes the express train is a sufficient condition
for her getting to Hogwarts. Since she didn’t get to
Hogwarts, it must be that she didn’t take the express train.
2. We’ll go to the picnic, unless we’ll play Twister. We
won’t play both frisbee and Twister. So, we will go to the
picnic, only if we’ll play frisbee.
1. (~D ~M)
M
-----------
∴
5. (~W ~Y)
~W
----------
∴
2. ~(L • ~S)
-------------
∴
6. (~T v ~C)
------------
∴
3. ~(V ~N)
-----------
∴
7. ~(X v ~U)
~X
----------
∴
4. ~(G • ~B)
~B
----------
∴
8. (~F ≡ J)
----------
∴
E. Construct truth tables for the following arguments and determine
whether valid or invalid. (You may use the short table method.)
5 points each x 2 = 10 points
D. Construct truth tables for the following formulas. 3 points each x 2 = 6 points
1 point each x 8 = 8 points F. Which expressions can be derived? If nothing follows, write “nil”.
1. ((O v M) v ~(T ⊃ Y))
~(O v M)
------------------------
∴
2. ~((A ⊃ ~B) v ~C)
------------------------
∴
3. ~((F ⊃ P) • Z)
~(F ⊃ P)
------------------------
∴
4. ((E • G) ≡ ~(H v L))
------------------------
∴
1. ~((F v R) (S • T))
~(F v ~S)
~T
2. ~((A v ~B) • (C D))
(E v X)
(E A)
(B ~X)
∴ C
H. Say whether the following arguments are VALID (and give a PROOF) or
INVALID (and give a REFUTATION).
5 points each x 2 = 10 points
3 points each x 4 = 12 points G. Derive everything that can be derived from the following premises. If nothing
follows, write “nil”.
1. The party was zany, unless it wasn’t loud.
Either the party was loud, or that the party was loud is not a necessary condition for it to be mad.
That the party was zany is not a sufficient condition of its being quiet. [Z, L, M]
2. If you don’t get excellent results then you aren’t noticeable, unless you are intelligent.
If you are adored, then you can’t both be intelligent and not get excellent results.
∴ You can’t both be adored and not get excellent results. [X, N, I, A]
I. Translate the following arguments into symbols. Say whether VALID (and give
a PROOF) or INVALID (and give a REFUTATION).
7 points each x 2 = 14 points
Scrap paper, if needed.
17-Sep
Syllogisms - Easier translations, star test, English
Arguments, harder translations
1-19; 3rd 1-17
24-5ep | Syllogisms - Deriving conclusions, Venn diagrams, 2030;3rd1827 | HL: BF, EF, AEM, AET, BH, BS,
idiomatic. Review BE
10ct | Test HZ: AHM, AHT, BD, BC, BI
Propositional - Easier translations, simple truth-tables,
equivalences, truth-evaluations, complex truth-tables
118-128; 3rd 112-
121
Propositional - truth-table test, truth-assignment test;
harder translations, idiomatic arguments
129-142; 3rd 122-
135
H3: CEM, CET, DTE, DFE, DTH,
DTM, DUE, DUM, DUH, DFM,
DFH
Proofs - Derivations: S-rules and I-rules. Easier and proofs
and refutations
143-162; 3rd 136-
156
Ha: DAE, DAM, DAH, CHM,
CHT, EI, ES, EE
Proofs - Harder proofs and refutations. Review
167-175; 3rd 161-
170
HS: FSE, FSH, FIE, FIH, FCE, FCH,
FTE, FTH, GEV, GE, GEC
HE: GHV, GHI, GHC, GMC
19-Nov
Quantificational - Easier translations
182-186; 3rd 182-
185
26-Nov
Quantificational - Easier proofs and refutations
187-194; 3rd 186-
193
H7: HEM, HET
2Me
HR IFV IF IEC
Sample Logic Quizzes
Propositional Logic Sample Quiz Page 5
We’ll be able to have class, only if either there’s chalk in
the room or else Gensler
ought chalk. There’s no chalk in
the room. So we won’t be able to have class. I say this, of
course, because Gensler didn’t
ing chalk.
If Gensler is healthy and there’s snow, then Gensler is
skiing.
Gensler is healthy.
Gensler isn’t skiing.
Á There’s no snow.
I’ll do poorly in logic. I’m sure of this because of the
following facts. First, I don’t do LogiCola. Second, I don’t
ead the book. Third, I spend my time playing Tetris. As-
suming that I spend my time playing Tetris and I don’t do
LogiCola, then, of course, if I don’t read the book then I’ll
do poorly in logic.
If you either remain silent or tell the truth, then the mur-
derer will know that your friend is hiding upstairs.
You won’t tell the truth.
Á The murderer won’t know that your friend is hiding
upstairs.
My tent will get wet and my food sack will get wet,
assuming that it rains. My tent will get wet. So my food
sack will also get wet.
Either I will stay home and it will be sunny, or I will go
ackpacking and it will rain.
I won’t go backpacking.
Á It will be sunny.
Translate into propositional logic
and say whether valid or invalid.
6 points
each
Propositional Logic Sample Quiz Page 6
((W Â F) Å ÀG) (C Ä (W Ã F))
G ÀW
ÀF ÀF
Á ÀW Á ÀC
(W Ä (F Ã N)) ((W Â ÀF) Ä ÀN)
ÀN N
Á ÀW Á F
((S Ã L) Ä (P Â H)) ((D Â W) Ã (B Â M))
ÀS ÀD
Á ÀP Á M
À(U Â ÀJ) (ÀG Ä ÀL) À(Q Ã L) (ÀZ Ã J) (ÀZ Â ÀL) À(P Ä ÀZ)
–––––––– ––––––––– –––––––– ––––––– –––––––– –––––––––
À(G Â H) (ÀH Ã ÀO) À(F Â ÀI) (O Ä ÀH) (U Ã ÀD) (ÀF Ä K)
ÀG O ÀI H ÀD K
––––––– –––––––––– –––––––– –––––––– –––––––– ––––––––
A is true only if B is true.
If not either A or B, then C but not D.
If A then B, or C.
A or B, but not both.
A is true, unless B and C are both true.
Valid o
invalid?
3 points
each
What letters (or negations of letters)
follow? Leave blank if nothing follows.
Translate into propositional logic wffs.
2 points
each
2 points each
Propositional Logic Sample Quiz Page 7
(ÀA Ä À(B Ã C))
(ÀA Ä (ÀB Ä C))
A
ÀC
Á ÀB
(A Å (A Â B))
Á (A Ä B)
Do a truth table
for this formula.
Test by the truth table method and
say whether valid or invalid.
4 points
4 points
each
Propositional Logic Sample Quiz Page 8
A N S W E R S T O P A G E 5
1. (A¹ Ä (Rº Ã Gº)) ≠ 1 Valid
ÀRº = 1
ÀGº = 1
Á ÀA¹ = 0
2. ((H¹ Â S¹) Ä Kº) ≠ 1 Valid
H¹ = 1
ÀKº = 1
Á ÀS¹ = 0
3. ÀLº = 1
ÀWº = 1
T¹ = 1
((T¹ Â ÀLº) Ä (ÀWº Ä Pº)) ≠ 1 Valid
Á Pº = 0
4. ((S? Ã Tº) Ä K¹) = 1 Invalid
ÀTº = 1
Á ÀK¹ = 0
5. (Rº Ä (T¹ Â Fº)) = 1 Invalid
T¹ = 1
Á Fº = 0
We let R=0 to make the first premise true.
6. ((H? Â Sº) Ã (Bº Â R?)) ≠ 1 Valid
ÀBº = 1
Á Sº = 0
A N S W E R S T O P A G E 6
1. ((W¹ Â Fº) Å ÀG¹) = 1 Invalid
G¹ = 1
ÀFº = 1
Á ÀW¹ = 0
2. (C¹ Ä (Wº Ã Fº)) ≠ 1 Valid
ÀWº = 1
ÀFº = 1
Á ÀC¹ = 0
3. (W¹ Ä (F¹ Ã Nº)) = 1 Invalid
ÀNº =