Proof Practice

1. A→(B&C)
2. (A&B)→C
3. A
1. B&C by 1,3 →out
2. A and B→C on two lines, both by 2 &out
3. A&B by 2 →out
4. None of the above.
1. A&(B→C)
2. (A&E)→D
3. B
1. C by 1,3 →out
2. A and B→C on two lines, both by 1 &out
3. A and E→D on two lines, both by 2 &out
4. None of the above.
1. C→(A&B)
2. (A&B)→D
3. A→E
1. D by 1,2 →out
2. A&B by 2 →out
3. A&B by 1 →out
4. None of the above.
1. R→(S&T)
2. (T→W)&R
3. T
1. S&T by 1,2 →out
2. T→W and R on two lines, both by 2&out
3. W by 2,3 →out
4. None of the above.
1. (R&S)→T
2. R
3. S
1. T by 1 →out
2. R&S by 1 →out
3. R&S by 2,3 &in
4. None of the above.
1. R→S
2. T→R
3. S
1. S by 1 →out
2. R by 1,2 →out
3. R by 1,3 →out
4. None of the above.
1. (E→F)→(G&H)
2. F
3. E→F
1. G&H by 1,3 →out
2. E by 2,3 →out
3. G and H on two lines, both by 1 &out
4. None of the above.
1. (E→F)→(G&H)
2. E
3. F
1. G&H by 1 →out
2. E&F by 2,3 &in
3. E→F by 2,3 →in
4. None of the above.
1. (E&F)→(G&H)
2. F&E
3. F→(I&J)
1. G&H by 1,2 →out
2. F and E on two lines, both by 2 &out
3. I&J by 2,3 →out
4. None of the above.
1. (E&F)→(G&H)
2. E&F
3. G→(I&J)
1. G&H by 1,2 →out
2. G and H on two lines, both by 1 &out
3. I&J by 3 →out
4. None of the above.
1. (E&F)→(G&H)
2. R→(S&(T&W))
3. (A→(B→C))&D
1. G&H by 1 →out
2. R and S&(T&W) on two lines, both by 2 &out
3. A→(B→C) and D on two lines, both by 3 &out
4. None of the above.
1. A→(B→C)
2. ((R&S)&(T&W))→Z
3. (A&(B→C))→D
1. E and B→C on two lines, both by 1 →out
2. R&S and (T&W)→Z on two lines, both by 2 &out
3. D by 1,3 →out
4. None of the above.
1. A→(B→C)
2. R→((S→T)&(W→Z))
3. (A→(B→C))→D
1. B→C by 1 →out
2. R→(S→T) and W→Z on two lines, both by 2 &out
3. D by 1,3 →out
4. None of the above.
1. M→(N→O)
2. M→((N→O)→(W→Z))
3. (N→O)→Z
1. W→Z by 1,2 →out
2. Z by 1,3 →out
3. N→O by 1,3 →out
4. None of the above.
1. (S→(R→T))→W
2. S→(R&T)
3. (R→(S→T))&(W→Z)
1. W by 1,2 →out
2. R→(S→T) and W→Z on two lines, both by 3 &out
3. Z by 1,3 →out
4. None of the above.
1. E
2. (D&E)→(B&C)
3. D
4. (B&H)→D
1. B&H by 3,4 →out
2. D&E and B&C by 2 →out
3. D&E by 1,3 &in
4. None of the above.
1. R
2. S→R
3. S→(M&N)
4. (S→R)→T
1. S by 1,2 →out
2. M&N by 2,3 →out
3. T by 2,4 →out
4. None of the above.
1. (R&S)→T
2. (T&W)→(A→B)
3. S&R
4. A→B
1. T by 1,3 →out
2. T&W by 2,4 →out
3. S and R on two lines, both by 3 &out
4. None of the above.
1. (G→H)&M
2. M→(A→B)
3. (G→H)→(S&T)
4. A→B
1. G→H and M on two lines, both by 1 &out
2. A→B by 1,2 →out
3. S&T by 1,3 →out
4. None of the above.
1. ((T→S)&M)→W
2. M
3. T→S
4. S
1. W by 1,3 →out
2. T by 3,4 →out
3. (T→S)&M by 2,3 &in
4. None of the above.
1. T→W
2. (S→(T→W))→B
3. S
4. T
1. B by 1,3 →out
2. S→(T→W) by 1,3 →in
3. W by 1,4 →out
4. None of the above.
1. A→B
2. ((B→A)&(C→D))→E
3. A→(B→C)
4. (A→(B→C))→D
1. B→A and (C→D)→E on two lines, both by 2 &out
2. C by 1,3 →out
3. D by 3,4 →out
4. None of the above.
1. N→O
2. ((M→L)&(N→O))→S
3. (T&W)→(M→L)
4. M→L
1. M→L and (N→O)→S on two lines, both by 2 &out
2. (M→L)&(N→O) by 1,4 &in
3. T&W by 3,4 →out
4. None of the above.
1. (N→O)→S
2. (M→L)→(N&O)
3. M&(N→O)
4. L→M
1. S by 1,3 →out
2. N&O by 2,4 →out
3. M and N→O on two lines, both by 3 &out
4. None of the above.
1. ((T→W)&S)→(A&B)
2. (T→W)→S
3. (A&B)→(C&D)
4. ((C&D)&S)→R
1. A&B by 1,2 →out
2. C&D by 1,3 →out
3. R by 2,3,4 →out
4. None of the above.

Proof Practice

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