Is it possible to check if this function is associative without checking all the cases?

Question

Given a boolean function with the following table:

$$\begin{matrix} {A}&{B}&{out}\\ {0}&{0}&{0}\\ {0}&{1}&{0}\\ {1}&{0}&{1}\\ {1}&{1}&{0} \end{matrix}$$

Is it possible to check if it's associative or not without checking all the cases?

Answer 1

The only way the result of $(AB)C$ could be $1$ is if $A=1, B= 0, C=0$.
However $A(BC)$ is also $1$ if $A=1, B=0, C=1$.
This disproves associativity:

$$(10)1=11=0\ne 1=10 = 1(01)$$