Logical Implication Question 
$A: \text{Humans are at most 12 feet tall}$
$B: \text{Humans are at most 9 feet tall}$

Neither implies the other.  A contradicts B and B contradicts A.
Am I correct?
 A: In modern logic terminology, back from the Aristotelian doctrine of the square of opposition, two sentences $\alpha$ and $\beta$ are said to be in a contradiction iff it is the case that $\alpha$ is true when $\beta$ is false and vice-versa, that is, $\alpha$ is false when $\beta$ is true.
This relation is found in both diagonals of the square:

Particularly, Two sentences are are 


*

*contradictory iff they cannot both be true and they cannot both be false

*contraries iff they cannot both be true but can both be false.

*subcontraries iff they cannot both be false but can both be true.


Particularly, B and A can be both false simultaneously, what disqualifies their logical relation as a contradiction. Still, B and A cannot be simultaneously true. Hence, B and A are contraries.

Now in regard of your question as to whether

A does not imply B and B does not imply A

Yes it is true. For the former, let humans be at most 12 feet tall. Then it follows humans are not at most 9 feet tall. For the latter, let humans be at most 9 feet tall. Then humans are not at most 12 feet tall. 
Most importantly, A and B are contraries, so remember that they cannot be both true. Then, if you assume one the other will be always false. The conclusion of our analysis is that both $A→B$ and $B→A$ cannot be the case.
A: 
  
*
  
*A:Humans are at most 12 feet tall
  
*B:Humans are at most 9 feet tall
  

We have: 


*

*A:= $\quad\forall h\in \operatorname{Humans}: \operatorname{tallness}(h)\leq 12$

*B:= $\quad\forall h\in \operatorname{Humans}: \operatorname{tallness}(h)\leq 9$


That is that neither statements' truth requires that the tallest possible human is of their given height, only that no human is taller that it.
So $B$ does not contradict $A$.   In fact there is a material implication: $B\to A$.   It is sufficient to know that if humans are at most $9$ feet tall, then we know humans are at most $12$ feet tall.
