# Proof by Inference

1. Mar 22, 2013

### ghostskwid

1. The problem statement, all variables and given/known data
Asked to either prove or make a counter example:

p ----> q
(q and r) ----> s
r
-------------------------------
p------> s

2. Relevant equations

3. The attempt at a solution

I am having trouble making the step to the law of syllogism I know I need to solve this. Can anyone help me with stepping this our using the rules of inference. I would greatly appreciate this thanks.

2. Mar 23, 2013

### CompuChip

Usually my first instinct when I need to prove an implication is to assume the precedent and prove the conclusion. I.e. in this case, try to prove

$p \implies q$
$(q \wedge r) \implies s$
$r$
$p$
-------------------------------
$s$

I think (hope) the next step is more obvious when put like this.

3. Mar 24, 2013

### ghostskwid

Thanks that, got the proof based on that info. :D