In the source's numerical illustration, one alternative is that the number is even or odd, while the other denies both alternatives within another disjunctive formulation.
The larger form is “Either the first disjunction, or the second disjunction.” Each of its two sides is itself a complete “or” structure. Hence this is a disjunction formed from two disjunctions.
The structural type of a sample and its actual truth are separate issues. We identify the full propositions under the outer disjunction before evaluating their truth.