SENTENTIAL LOGIC
TRANSLATION AND SHOWING VALIDITY USING DEDUCTION
Write out the dictionary. Translate each sentence to form an argument in
sentential logic. Construct a deduction to prove the argument valid.
Either the blood test and the EKG are not both accurate or else the patient
has a heart disorder. Either the blood test was accurate or else neither the
nurse nor the lab technician acted competently. The nurse acted
competently. Therefore, either the EKG is not accurate or else the patient
had a heart disorder. (B, E, P, N, L)
To deduce: ~E V P
1.
~(B & E) V P
Premise
2.
B V ~ (N V L)
Premise
3.
N
Premise
4.
B V (~N & ~L)
2 DeMorgans
5.
(B V ~N) & (B V ~L)
4 Distribution
6.
B V ~N
5 Simplify
7.
B
3, 6 DS
8.
P V ~(B & E)
1 Commute
9.
P V (~B V ~E)
8 DeMorgans
10.
P V (~E V ~B)
9 Commute
11.
(P V ~E) V ~B
10 Association
12.
P V ~E
7, 11 DS
13.
~E V P
12 Commute
Gustason, Elementary Symbolic Logic, Ch 3, p. 94