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10-56
107.
Determine whether the following is valid or invalid:
In a class like this, it’s necessary to work a lot of problems on your own in order to be
familiar with the material, and such familiarity is necessary to do well in the exams. So if
you work a lot of problems on your own, you’ll do well on the exams.
Valid.
108.
Determine whether the following is valid or invalid:
It’s not true that Alberto and John will both attend the meeting. I did learn, however, that if
either Susan or Allene goes, John plans to go for sure. Therefore, if Alberto goes, it means
neither Susan nor Allene is going.
Valid.
109.
Determine whether the following is valid or invalid:
If the current economic policies were to put an end to the recession, then the
administration would deserve a round of applause. But there can be no end to the
recession without the creation of a large number of decent-paying jobs. It follows, then,
that the only way the administration is going to get a round of applause is if a large
number of decent-paying jobs get created.
Invalid.
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110.
Determine whether the following is valid or invalid:
I finally discovered the mystery of why hard beds are good for you. Here’s the story: If you
have a hard bed, then you cannot stay comfortable for long periods, and when you can’t
stay comfortable for long periods, you roll around a lot. If you roll around a lot, then your
joints don’t ache from being in one position for too long. Therefore, if your joints ache in
the morning from sleeping too long in one position, then you don’t have a hard bed.
Valid.
111.
Determine whether the following is valid or invalid:
Either the bank made a mistake, or none of this month’s deposits have been recorded. If
our accountant is correct, then all the accounts have been reconciled. If it is not the case
that none of the month’s deposits has been recorded, then all the accounts could not have
been reconciled. I have checked with our accountant, and he is indeed correct. Therefore,
the only alternative is that the bank made a mistake.
Valid.
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112.
Using the letters provided below, symbolize this claim: "If we are leaving next week, we'll
have to book our flight today."
A = We book our flight today.
S = We are leaving next week.
S → A
113.
Using the letters provided below, symbolize this claim: "If they confirm the meeting today,
Jonah will buy the necessary equipment."
A = Jonah will buy the necessary equipment.
S = They confirm the meeting today.
S → A
114.
Using the letters provided below, symbolize this claim: "We can go camping only if our
packages arrive today."
A = We go camping.
S = Our packages arrive today.
A → S
115.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
S v R
S → T/∴ T → R
S = T
R = F
T = T
116.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
A → (Z v ~D)
D & M
~M v W/∴ ~A & W
A = T
Z = T
D = T
M = T
W = T
117.
Use the short truth-table method to determine whether the following is valid or invalid:
Z → K
J → O
K v O/∴ Z v J
Invalid: Z = F
J = F
Make either K or O = T
118.
Use the short truth-table method to determine whether the following is valid or invalid:
E → N
N → X
X → O
E/∴ O v D
119.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there are only two such assignments).
(A & Y) → (I v J)
A & Y/∴ I & J
A = T A= T
Y = T Y = T
I = T I = F
J = F J = T
120.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
~U & G
(H v C) → U/∴ C v G
U = F
G = F
H = F
C = F
121.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
~P → ~A
~W → (P & A)/∴ W
P = T
A = T
W = F
122.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
(B & V) → N
J → ~N/∴ J → ~B
B = T
V = F
N = F
J = T
123.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
B v A
~B → ~N/∴ N → A
A = F
B = T
N = T
124.
Use the short truth-table method to determine whether the following is valid or invalid:
Z → K
~O v J
N → M
Q → R
Z v O
N v Q/∴ (K v J) v (M v R)
Valid.
125.
Use the short truth-table method to determine whether the following is valid or invalid:
A → (Z & L)
L → (W v G)
~W v (D & ~E)
A/∴ ~E
Invalid: A = T
Z = T
L = T
G = T
W = F
D = T or F
E = T
126.
Use the short truth-table method to determine whether the following is valid or invalid:
A → Z
~(Z & ~L)
~L v G
~(G & ~W)
W/∴ A
Invalid: A = F OR A = F OR A = F
Z = F Z = T Z = F
L = F L = T L = T or F
G = F G = T G = T
W = T W = T W = T
127.
Use the short truth-table method to determine whether the following is valid or invalid:
~J v ~M
~(Y → G)
~(~H v ~J)
~(Y & H) v (J → M)/∴ ~Y
Invalid: Y = T
H = T
M = F
G = F
128.
Use the short truth-table method to determine whether the following is valid or invalid:
J → U
C → K
~(~J & ~C)/∴ ~B → (U & ~K)
Valid.
129.
Determine whether the following symbolized argument is valid or invalid. If invalid, provide
a counterexample; if valid, construct a deduction.
(E v N) → (X & O)
~X/∴ ~N
Valid. The deduction could look like this:
1. (E v N) → (X & O)
2. ~X/∴ ~N
3. ~X v ~O 2, ADD
4. ~(X & O) 3, DEM
5. ~(E v N) 1,4, MT
6. ~E & ~N 5, DEM
7. ~N 6, SIM
130.
Determine whether the following symbolized argument is valid or invalid. If invalid, provide
a counterexample; if valid, construct a deduction.
A v ~Z
G → Z
~A
~G → ~H/∴ H
Invalid.
A = F
Z = F
G = F
H = F
131.
Determine whether the following symbolized argument is valid or invalid. If invalid, provide
a counterexample; if valid, construct a deduction.
(I → K) & M
M → (K → W)
~W/∴ ~K
Valid. The deduction could look like this:
1. (I → K) & M
2. M → (K → W)
3. ~W/∴ ~K
4. (M & K) → W 2, EXPORT
5. ~(M & K) 3,4, MT
6. ~M v ~K 5, DEM
7. M 1, SIM
8. ~K 6,7, DA
132.
Determine whether the following symbolized argument is valid or invalid. If invalid, provide
a counterexample; if valid, construct a deduction.
(B v D) → F
~F/∴ ~D
Valid. The deduction could look like this:
1. (B v D) → F
2. ~F/∴ ~D
3. ~(B v D) 1,2, MT
4. ~B & ~D 3, DEM
5. ~D 4, SIM
133.
Using the letters provided below, symbolize this claim: "If we leave now, we can either
take the bus or the train."
A = We leave now.
S = We take the bus.
P = We take the train.
(S v P) → A
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