The first three columns are simply a systematic listing of all possible combinations of T and F for the three statements (do you see how you would list the 16 possible combinations for four statements?). The next two columns are determined by the values of \(P\text{,}\) \(Q\text{,}\) and \(R\) and the definition of implication. Then, the last column is determined by the values in the previous two columns and the definition of \(\vee\text{.}\) It is this final column we care about.
in-context