1. The problem is to find the union of two sets and illustrate it with a Venn diagram. 2. The union of two sets $A$ and $B$ is defined as the set containing all elements that are in $A$, or in $B$, or in both. It is denoted as: $$A \cup B = \{x : x \in A \text{ or } x \in B\}$$ 3. To visualize this, we draw two overlapping circles representing sets $A$ and $B$. The union includes all areas covered by both circles. 4. For example, if $A = \{1,2,3\}$ and $B = \{3,4,5\}$, then: $$A \cup B = \{1,2,3,4,5\}$$ 5. The Venn diagram shows two circles overlapping, with the entire area of both circles shaded to represent the union. 6. This means any element in either circle is included in the union.