Show that there are exactly two truth assignments for the variables P, Q, R, S that satisfy the following formula: (¬P OR Q) AND (¬Q OR R) AND (¬R OR S) AND (¬S OR P)

Problem 3.1.
Show that there are exactly two truth assignments for the variables \( \mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S} \) that satisfy the following formula:
\[
(\bar{P} \text { OR } Q) \text { AND }(\bar{Q} \text { OR } R) \text { AND }(\bar{R} \text { OR } S) \text { AND }(\bar{S} \text { OR } P)
\]

Hint: A truth table will do the job, but it will have a bunch of rows. A proof by cases can be quicker; if you do use cases, be sure each one is clearly specified.