Proof Practice
Imagine that the lines below are the premises of a proof. How would you start? Choose the best answer.

1. A→(B&C)
2. (A&B)→C
3. A

B&C by 1,3 →out

A and B→C on two lines, both by 2 &out

A&B by 2 →out

None of the above.

1. A&(B→C)
2. (A&E)→D
3. B

C by 1,3 →out

A and B→C on two lines, both by 1 &out

A and E→D on two lines, both by 2 &out

None of the above.

1. C→(A&B)
2. (A&B)→D
3. A→E

D by 1,2 →out

A&B by 2 →out

A&B by 1 →out

None of the above.

1. R→(S&T)
2. (T→W)&R
3. T

S&T by 1,2 →out

T→W and R on two lines, both by 2&out

W by 2,3 →out

None of the above.

1. (R&S)→T
2. R
3. S

T by 1 →out

R&S by 1 →out

R&S by 2,3 &in

None of the above.

1. R→S
2. T→R
3. S

S by 1 →out

R by 1,2 →out

R by 1,3 →out

None of the above.

1. (E→F)→(G&H)
2. F
3. E→F

G&H by 1,3 →out

E by 2,3 →out

G and H on two lines, both by 1 &out

None of the above.

1. (E→F)→(G&H)
2. E
3. F

G&H by 1 →out

E&F by 2,3 &in

E→F by 2,3 →in

None of the above.

1. (E&F)→(G&H)
2. F&E
3. F→(I&J)

G&H by 1,2 →out

F and E on two lines, both by 2 &out

I&J by 2,3 →out

None of the above.

1. (E&F)→(G&H)
2. E&F
3. G→(I&J)

G&H by 1,2 →out

G and H on two lines, both by 1 &out

I&J by 3 →out

None of the above.

1. (E&F)→(G&H)
2. R→(S&(T&W))
3. (A→(B→C))&D

G&H by 1 →out

R and S&(T&W) on two lines, both by 2 &out

A→(B→C) and D on two lines, both by 3 &out

None of the above.

1. A→(B→C)
2. ((R&S)&(T&W))→Z
3. (A&(B→C))→D

E and B→C on two lines, both by 1 →out

R&S and (T&W)→Z on two lines, both by 2 &out

D by 1,3 →out

None of the above.

1. A→(B→C)
2. R→((S→T)&(W→Z))
3. (A→(B→C))→D

B→C by 1 →out

R→(S→T) and W→Z on two lines, both by 2 &out

D by 1,3 →out

None of the above.

1. M→(N→O)
2. M→((N→O)→(W→Z))
3. (N→O)→Z

W→Z by 1,2 →out

Z by 1,3 →out

N→O by 1,3 →out

None of the above.

1. (S→(R→T))→W
2. S→(R&T)
3. (R→(S→T))&(W→Z)

W by 1,2 →out

R→(S→T) and W→Z on two lines, both by 3 &out

Z by 1,3 →out

None of the above.

1. E
2. (D&E)→(B&C)
3. D
4. (B&H)→D

B&H by 3,4 →out

D&E and B&C by 2 →out

D&E by 1,3 &in

None of the above.

1. R
2. S→R
3. S→(M&N)
4. (S→R)→T

S by 1,2 →out

M&N by 2,3 →out

T by 2,4 →out

None of the above.

1. (R&S)→T
2. (T&W)→(A→B)
3. S&R
4. A→B

T by 1,3 →out

T&W by 2,4 →out

S and R on two lines, both by 3 &out

None of the above.

1. (G→H)&M
2. M→(A→B)
3. (G→H)→(S&T)
4. A→B

G→H and M on two lines, both by 1 &out

A→B by 1,2 →out

S&T by 1,3 →out

None of the above.

1. ((T→S)&M)→W
2. M
3. T→S
4. S

W by 1,3 →out

T by 3,4 →out

(T→S)&M by 2,3 &in

None of the above.

1. T→W
2. (S→(T→W))→B
3. S
4. T

B by 1,3 →out

S→(T→W) by 1,3 →in

W by 1,4 →out

None of the above.

1. A→B
2. ((B→A)&(C→D))→E
3. A→(B→C)
4. (A→(B→C))→D

B→A and (C→D)→E on two lines, both by 2 &out

C by 1,3 →out

D by 3,4 →out

None of the above.

1. N→O
2. ((M→L)&(N→O))→S
3. (T&W)→(M→L)
4. M→L

M→L and (N→O)→S on two lines, both by 2 &out

(M→L)&(N→O) by 1,4 &in

T&W by 3,4 →out

None of the above.

1. (N→O)→S
2. (M→L)→(N&O)
3. M&(N→O)
4. L→M

S by 1,3 →out

N&O by 2,4 →out

M and N→O on two lines, both by 3 &out

None of the above.

1. ((T→W)&S)→(A&B)
2. (T→W)→S
3. (A&B)→(C&D)
4. ((C&D)&S)→R

A&B by 1,2 →out

C&D by 1,3 →out

R by 2,3,4 →out

None of the above.