I am stuck in this question. Please help.

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- Aug 21st 2011, 12:16 AMMathsNewbie0811Determine whether he following logic argument is valid.
I am stuck in this question. Please help.

Attachment 22097 - Aug 21st 2011, 12:50 AMMATHNEMRe: Need help in solving this question
We have to deduce $\displaystyle t\rightarrow w$, which is equivalent to $\displaystyle \neg w \rightarrow \neg t$, from:

$\displaystyle \\ \neg p \rightarrow (r \wedge \neg s) \quad (1) \\ t \rightarrow s \quad (2) \\ u \rightarrow \neg p \quad (3) \\ \neg w \quad (4) \\ u \vee w \quad (5) \\ u \quad (6) \mbox{ From 5 and 4} \\ \neg p \quad (7) \mbox{ From 3 and 6 } \\ r \wedge \neg s \quad (8) \mbox{ From 1 and 7 } \\ \neg s \quad (9)\mbox{ From 8 } \\ \neg t \quad (10) \mbox{ From 2 and 9 } \\ \neg w \rightarrow \neg t \quad \mbox{ From 4 and 10 }$

Hence, it's a valid argument. Hope this helps you. - Aug 21st 2011, 01:36 AMterrorsquidRe: Need help in solving this question
How do you get (9) from 8? Truth table gives F T F F which is something different.

- Aug 21st 2011, 01:53 AMAlso sprach ZarathustraRe: Need help in solving this question
$\displaystyle \frac{\alpha \land \beta}{\alpha } $

and,

$\displaystyle \frac{\alpha \land \beta}{\beta }$

Edit:

Proof:

$\displaystyle \alpha \land \beta$ true only when $\displaystyle \alpha$ and $\displaystyle \beta $ are both true. Therefor, if $\displaystyle \alpha \land \beta$ true at particular reference, so are $\displaystyle \alpha$ and $\displaystyle \beta$ are true in that particular reference.

And we can write, $\displaystyle \alpha \land \beta \models \alpha$ and $\displaystyle \alpha \land \beta \models \beta$ - Aug 21st 2011, 02:03 AMterrorsquidRe: Need help in solving this question
- Aug 21st 2011, 02:42 AMterrorsquidRe: Need help in solving this question
- Aug 21st 2011, 11:43 AMMATHNEMRe: Need help in solving this question
We have correctly inferred that $\displaystyle r \wedge \sim s$ is true, but this implies that $\displaystyle r$ is true and so is $\displaystyle \sim s$.

Simplification - Wikipedia, the free encyclopedia

I'm sorry I couldn't find something else. - Aug 21st 2011, 11:47 AMPlatoRe: Need help in solving this question
A word about not and LaTeX.

[tex]\neg P[/tex] gives $\displaystyle \neg P $