The question:
Let $P$, $Q$, and $R$ be statements. Determine whether or not the two expressions in each pair are logically equivalent. In each case, demonstrate that your answer is correct.
a.) $(P ∧Q) ∧R, P ∧(Q ∧R)$
My attempt using truth table:
\begin{array}{|c|c|c|c|} \hline P& Q & P ∧ Q& R \\ \hline T& T& T&T\\ \hline F& T & F&F\\ \hline T& F & F&F\\ \hline F& F & F&F\\ \hline \end{array}
\begin{array}{|c|c|c|c|} \hline Q& R & Q ∧ R& P \\ \hline T& T& T&T\\ \hline F& T & F&F\\ \hline T& F & F&F\\ \hline F& F & F&F\\ \hline \end{array}
Therefore, they are equivelent.
Is this the correct method/approach to showing that the statements are correct using truth tables?
It is correct. Although, you might use the fact that $\land$ is associative unless the problem specifically doesn't want you to do that. If that is the case, then the truth table is the only way.