Is This Discrete Mathematics Argument Valid?

[gEOdude]

Homework Statement

Hey guys I am having a bit of a difficult time with this question, if some one could help me out it would be appreciated, thanks.

Consider the following argument. "If the weather is fine, and the train is early, then the dog will sit on the tuckerbox. The train will be early, (but) also there will be rain. So the dog will not sit on the tuckerbox."Let W mean "the weather will be fine", E mean "the train will come early" and D mean "the dog will sit on the tuckerbox". (THE QUESTION IS ATTATCHED BELOW)

Homework Equations

The Attempt at a Solution

I tried working out the equation and I got this: I get the following compound propisiton arguments like this for first and second premisis and conclusion: (W v E -> D) ^ (E ^ ~W) -> ~D. I also know that T appears in rows B,D,F and H of the last column and this was confirmed by my teacher. Now I know how to construct the truth table but i keep getting the question wrong, i do not know what I am doing wrong, help would be appreciated.

 

[HallsofIvy]

It is impossible to say what you are doing wrong when you don't tell us what you are doing! What wrong answers are you getting?

 

[gEOdude]

i DON't know what the answer is to the question I've put, that's all and I am entering the formula above into a truth table that's what I am doing if someone could tell me the question it would be great.

 

[gEOdude]

this is what I've done

 

[gEOdude]

It is impossible to say what you are doing wrong when you don't tell us what you are doing! What wrong answers are you getting?