Question 1190080
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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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