A Couple of Logic Problems That I'm Struggling With........

[deemanw]

I can't collect my terms and prove the hint below?????? Please Help?????

> problem#1
>
> justify validity:
> ^ - "and"
> a->(b ^ c)
> ~b V d
> (e->~f)->~d
> b->(a ^ ~e)
> -----------
> therefore b->e
>
Hint, therefore b -> ~b

> problem#2
>
> prove valid/invalid:
>
> a->b
> b->~c
> ~a->d
> ~c->e
> a V ~a
> ----------
> therefore e
>
Hint, invalid.

 

[pka]

Here is an outline of #1. You must fill in the reasons that your text gives.


\(\displaystyle \
\begin{array}{l}
\left[ 1 \right]\;a \to \left( {b \wedge c} \right) \\
\left[ 2 \right]\;\~b \vee d \\
\left[ 3 \right]\;\left( {e \to \~f} \right) \to \~d \\
\left[ 4 \right]\;b \to \left( {a \wedge \~e} \right) \\
\\
\left[ 5 \right](b \to d)\quad \left[ 2 \right] \\
\left[ 6 \right]\;d \to \~(e \to \~f)\quad \left[ 3 \right] \\
\left[ 7 \right]\;b \to \~(e \to \~f)\quad \left[ {5\& 6} \right] \\
\left[ 8 \right]\;\left( {\~b \vee e} \right) \wedge \left( {\~b \vee f} \right)\quad \left[ 7 \right] \\
\left[ 9 \right]\;\left( {\~b \vee e} \right)\quad \left[ 8 \right] \\
\;\left( {b \to e} \right)\quad \left[ 9 \right] \\
\end{array}\)

 

[deemanw]

hey thanks!!!!!!! :l :lol:

the hints may not be correct as it appears you've shown for problem 1.