NFL, DNF-style

I don’t normally link to sites that require registration, such as the New York Times, but of the final week of the NFL regular season features both a reference to Boolean algebra and an explanation of how the Broncos can get into the playoffs in disjunctive normal form:

George Boole, the 19th-century philosopher, developed Boolean algebra, the system of precisely defined conjunctions and operators that made possible computer logic and playoff tie-breaker scenarios. Without Boole, it would be impossible to explain that the Broncos can make the playoffs with a win AND {(a Jets loss AND losses by [Ravens or Steelers]) OR (a Jets loss AND Texans win) OR (a Ravens loss AND [Steelers loss OR Texans win])}. It would be even be more difficult to explain that the Broncos can also clinch with a loss AND {(Steelers AND Ravens AND Texans AND Jaguars losses) OR (Steelers AND Ravens AND Texans AND Jets losses) OR (Steelers AND Ravens AND Jaguars AND Jets losses) OR (Steelers AND Jaguars AND Jets AND Texans losses) OR (Jets AND Jaguars AND Texans AND Ravens losses)}. We all owe Boole a parenthetical debt of gratitude for making things so crystal clear.