If I understand the gates (i.e., A connected to an OR-gate and B connected to an AND-gate) and connections correctly, we might express it as a statement:

Q = min(max(A, X), B')

Where B' = 1-B, X is unknown, and true inputs are 1, false inputs 0. There are four possible cases.

Spoiler:

In three of the cases the output is wholly determined by the values of A and B, regardless of what X is. The one case that is mysterious is whenever A and B are both false. But if I think of this in terms of electric circuits, then if both A and B have no current, then there is no possible way for X to have current. Therefore, we can just define X = 0 there. I don't know if that is the current assessment, but I find that diagram a bit odd. These were my thoughts on it.

I noticed a second thought just now. By what I said above, X = A will produce the same results. Redefine the diagram in those terms and see what you think.