Assignment 25407

Complete the following proofs. They can be done in one step using the rules
from 7.1 and 7.2 of your text. 14
points.
Example:
1. A
2. A>B / B
3. B 1,2
MP ßYou add this line
1.
G > H
2.
~H /
~G
3.

1.
J > K
2.
K > (L * M) /
J > (L * M)
3.

1.
O v P
2.
~O /
P
3.

1.
R * S /
S
2.

1.
R
2.
T /
R * T
3.

1.
W /
W v X
2.

1.
(X > Y) * (Y
> Z)
2.
X v Y /
Y v Z
3.

1.
(C * D) > (E v F)
2.
C * D /
E v F
3.

1.
(G > H) > (I * J)
2.
~(I * J) /
~(G > H)
3.

1.
(J v K) > ~(L > M)
2.
~(L > M) > N / (J v K) > N
3.

1.
O v (P v Q)
2.
~(P v Q) /
O
3.

1.
R * (S v T) /
R
2.

1.
R > S
2.
S > (T v U) /
(R > S) * (S > (T v U))
3.

1.
W * X /
(W * X) v (X * Y)
2.

Two-Step Proofs.
Complete the following proofs.
They can be done in two steps using the rules from 7.1 and 7.2 of your
text. There may be more than one way to
do some of the proofs. 14 points.
Example:
1. A
2. A
> B
3. B
> C / C
4.
B 1,2 MP ß You add either version
à 4. A > C 2,3 HS
5.
C 3,4 MP of
lines 4 and 5 5. C 1,4
MP
1.
~C
2.
A > B
3.
B > C /
~A
1.
D > E
2.
F > G
3.
D v F /
E v G
1.
A * B /
A v C
1.
(H v I) > J
2.
H /
J
1.
(H * I) > J
2.
H
3.
I /
J
1.
H > (I * J)
2.
H /
J
1.
(K * L) v (M * N)
2.
~(K * L) /
N
Proofs with Translation. Translate the following proofs into symbols,
using the letters suggested. Each letter
should stand for a simple sentence. Then
do the proofs. 12 points.
Example:
If we are morally responsible
for our actions, we have free will. If
we are not morally responsible for our actions, jails should be
emptied. We don’t have free will. Therefore, jails should be emptied.
(M, F, J)
You write
everything that follows:
M = We are morally responsible
for our actions
F = We have free will
J = Jails should be emptied.
1.
M > F
2.
~M > J
3.
~F /
J
4.
~M 1,3 MT
5.
J 2,4
MP
1. Either
the mind is identical to the brain, or it is immaterial. If the mind is immaterial, it doesn’t make
any difference. The mind makes a
difference. Therefore, the mind is
identical to the brain. (B, I, D)
2. If
there is not an afterlife, then all is hopeless. If all is hopeless, despair is the right
attitude. Despair is not the right
attitude. Therefore, there is an
afterlife. (A, H, D)