TAOCP 7.2.2.2 Exercise 156
A pure literal $l$ is a special case of an autarky because the partial assignment that sets $l=1$ and leaves all other variables unset satisfies every clause containing the variable $|l|$.
Section 7.2.2.2: Satisfiability
Exercise 156. [05] [05] Why is a pure literal a special case of an autarky?
Verified: yes
Solve time: 1m14s
A pure literal $l$ is a special case of an autarky because the partial assignment that sets $l=1$ and leaves all other variables unset satisfies every clause containing the variable $|l|$. Since $l$ is pure, no clause contains $\bar{l}$, so every clause touched by this assignment contains the satisfied literal $l$.
Thus the one-variable partial assignment ${l}$ satisfies all clauses it affects, which is exactly the condition for an autarky. Therefore every pure literal gives an autarky of size one. Conversely, an autarky need not consist of a pure literal, since several assigned variables may cooperate to satisfy the clauses they touch.