How to identify rules of inference that establishes validity? I've been trying to determine an explanation for the falsity of a logical statement for some time now and I've had no luck in figuring out exactly how to go about it. The two part question goes as follows:    

Consider the arguments below. If the argument is valid, identify the rule of
inference that establishes its validity. If not, explain why.

a. If Robert understands the concepts correctly, he will be able to finish his
assignment in two hours. Robert finished his assignment in more than two
hours. Therefore, Robert did not understand the concepts correctly.

b. If taxes increase, the housing market will decrease. Taxes are not
increasing. Therefore, the housing market will not decrease.


Perhaps I'm misunderstanding the way to determine the falsity of a logical statement? Any help is appreciated.
The "logical form" of the premise of a) is :


  if $p$, then $q$.


The following is a valid argument :


  $p \rightarrow q \vDash \lnot q \rightarrow \lnot p$,


thus, from the above premise we can correctly conclude with :


  if not $q$, then not $p$


which is exactly the conclusion of a).

The argument in b) is not valid, because :


  $p \rightarrow q \nvDash \lnot p \rightarrow \lnot q$; 


thus, from the premise : if $p$, then $q$, we cannot conclude with : if not $p$, then not $q$.
a) is valid by modus tollens. Because recall, modus tollens is,

P → Q, ~Q  |- ~P


The argument is identical