If 1 means there is room X available, 0 it is not available, ∨/ means if return 1, there is at last one free room. If return 0, there is no room available
I see a problem here for ⌹. It seems a⌹b would find the solution of linear sys coefficients in b matrix with result a array so linear system bx=a. If the solution of bx=a exist and is only 1, all ok. What it would return if the system has no solution? What would return if the system has infinite solutions?
