The statement pattern $[(p \wedge q) \rightarrow (\sim p \vee r)] \vee [(\sim p \vee r) \rightarrow (p \wedge q)]$ is

Let $A = p \wedge q$ and $B = \sim p \vee r$.

The given statement pattern can be written as $(A \rightarrow B) \vee (B \rightarrow A)$.

Using the logical equivalence $X \rightarrow Y \equiv \sim X \vee Y$, the expression becomes:

$(\sim A \vee B) \vee (\sim B \vee A)$

Using the commutative and associative properties of disjunction, we can rearrange the terms as:

$(\sim A \vee A) \vee (\sim B \vee B)$

We know that for any statement $X$, $\sim X \vee X \equiv T$ (where $T$ represents a tautology).

Substituting this into the expression, we get:

$T \vee T \equiv T$

Therefore, the given statement pattern is a tautology.

Answer: a tautology