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: [ (ar{P} ext { OR } Q) ext { AND }(ar{Q} ext { OR } R) ext { AND }(ar{R} ext { OR } S)

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.