##\left(x_2x_3\right)\in\{0,1\}^2## just means that the string ##x_2x_3## is from the set of all 2-tuples of numbers belonging to ##\{0,1\}##. The notation is similar to how you would use ##R^n## for a coordinate space, just replace ##R## with ##\{0,1\}## and n with 2.
Then, as you presumed, the...