Representation Math Example 1

Solution

1. 1
   Roster: $A=\{1,2,\ldots,10\}$, $B=\{2,4,6,8,10\}$, $C=\{1,3,5\}$.
2. 2
   Set-builder: $B=\{x \in A : x \text{ is even}\}$, $C=\{x \in A : x \text{ is odd and } x \le 5\}$.
3. 3
   Venn diagram: Draw a rectangle for $A$. Inside, draw circle $B$ (even numbers) and circle $C$ (odd $\le 5$). They do not overlap. Elements 7,9 are in $A$ but outside both circles.