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Arrow Out Practice
Imagine that these are the first two lines of a proof. What could you write on a third line using the →Out rule?
1. A→B
2. A
?
A
?
B
?
A→B
?
→out cannot be applied
1. R
2. R→S
?
R
?
S
?
S→R
?
→out cannot be applied
1. M
2. M→T
?
T
?
M
?
T→M
?
→out cannot be applied
1. A→B
2. B
?
A
?
B
?
A→B
?
→out cannot be applied
1. G
2. H→G
?
H
?
G→H
?
G
?
→out cannot be applied
1. S
2. S→(R→T)
?
R→T
?
T
?
S→R
?
→out cannot be applied
1. R→(S&T)
2. S&T
?
R
?
T
?
R→S
?
→out cannot be applied
1. (E&F)→G
2. E&F
?
G
?
F→G
?
E
?
→out cannot be applied
1. M
2. M→(N→O)
?
O
?
M→N
?
N→O
?
→out cannot be applied
1. W→Z
2. (W→Z)→B
?
Z→B
?
B
?
W
?
→out cannot be applied
1. (R→M)→E
2. R→M
?
R
?
E
?
M→E
?
→out cannot be applied
1. (N&R)→(S&T)
2. N
?
S&T
?
R
?
N&R
?
→out cannot be applied
1. (A&B)→(S&T)
2. A&B
?
S
?
T
?
S&T
?
→out cannot be applied
1. D→(B&(C→H))
2. D
?
B&(C→H)
?
C→H
?
H
?
→out cannot be applied
1. R&S
2. W→((R&S)→T)
?
T
?
W
?
(R&S)→T
?
→out cannot be applied
1. (R→S)&T
2. R
?
S
?
S&T
?
T
?
→out cannot be applied
1. (K→J)→M
2. K→J
?
M
?
K
?
J
?
→out cannot be applied
1. (K→J)→M
2. M
?
K
?
J
?
K→J
?
→out cannot be applied
1. H&N
2. (H&N)→(R→Z)
?
R
?
Z
?
R→Z
?
→out cannot be applied
1. (H→N)→R
2. (H→N)→(R→Z)
?
Z
?
R
?
N→(R→Z)
?
→out cannot be applied
1. ((W→H)→M)→G
2. W
?
(H→M)→G
?
H→(M→G)
?
M→G
?
→out cannot be applied
1. W→((H→M)→G)
2. W
?
H→(M→G)
?
(H→M)→G
?
G
?
→out cannot be applied
1. A
2. A→(B→(C→D))
?
(B→C)→D
?
B→(C→D)
?
C→D
?
→out cannot be applied
1. (W→H)→M
2. ((W→H)→M)→G
?
H
?
M→G
?
G
?
→out cannot be applied
1. R→((A&R)&D)
2. (A&R)&D
?
R
?
A&R
?
D
?
→out cannot be applied
1. (R→(S&T))→(A&F)
2. R→(S&T)
?
A&F
?
S&T
?
(S&T)→(A&F)
?
→out cannot be applied
1. M→((A&B)→(N&E))
2. M→(A&B)
?
N&E
?
A&B
?
(A&B)→(N&E)
?
→out cannot be applied
1. M→((A&B)→(N&E))
2. M
?
N&E
?
A&B
?
(A&B)→(N&E)
?
→out cannot be applied
1. ((R&S)→T)→(N&M)
2. ((R&S)→T)→N
?
M
?
N
?
(R&S)→T
?
→out cannot be applied
1. (R&S)→T
2. ((R&S)→T)→(N&M)
?
T
?
R&S
?
N&M
?
→out cannot be applied
1. (S&R)→T
2. R&S
?
T
?
R→T
?
S→T
?
→out cannot be applied
1. (G&H)→(I&J)
2. H&G
?
I&J
?
G&H
?
J
?
→out cannot be applied
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