1. **Problem:** Compute $A \cup B$ where $A = \{a, b, c, g\}$ and $B = \{d, e, f, g\}$. 2. **Formula:** The union of two sets $A$ and $B$ is defined as $A \cup B = \{x : x \in A \text{ or } x \in B\}$. 3. **Step-by-step solution:** - List elements of $A$: $a, b, c, g$. - List elements of $B$: $d, e, f, g$. - Combine all unique elements from both sets: $a, b, c, g, d, e, f$. 4. **Final answer:** $$A \cup B = \{a, b, c, d, e, f, g\}$$