Question 1190080: 1.(N V O) ⊃ (C • D)
2.(D V K) ⊃ (P V ~C)
3.(P V G) ⊃ (N • D)
∴ ~N
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
T = true
F = false
To see if we have an invalid argument, we have to try to make the conclusion false and all premises true.
If ~N = F, then N = T
If N = T, then N v O = T
To make (N v O) -> (C * D) true, the C*D portion must be true. This breaks down to C = T and D = T.
Because D = T, we can say D v K = T
This leads to P v ~C needing to be true
C = T tells us ~C = F
So P = T must be the case if we want P v ~C = T
If P = T, then P v G = T regardless if G is true or false
The N*D portion is true because both N = T and D = T together. So (P v G) -> (N*D) is true overall.
In short, if we have the following
N = T
C = T
D = T
P = T
then all the premises will be true, but the conclusion ~N would be false.
Therefore, this argument is invalid.
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