SOLUTION: 1.(I.E)>C 2.C>~C / I

Question 1136119: 1.(I.E)>C
2.C>~C
/ I

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The argument is invalid

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Explanation:

Consider these three facts
* logical statement I = F
* logical statement E = T
* logical statement C = F
where F = false, T = true

If those three facts are set up, then
this means I & E = F & T = T
and it means (I & E) > C = F > F = T
So the first premise (I & E) > C is true here

Furthermore, C > ~C = F > ~F = F > T = T
The second premise C > ~C is true here

However, the conclusion I is false as set above in the initial conditions.

Because we have all true premises but they lead to a false conclusion, this means that we do not have a valid argument.

Here is what the truth table looks like to set up this argument. The blue columns are premises. The green column is the conclusion. The row marked with a red box shows the true premises leading to a false conclusion.

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