Chapter 2 - Set Theory - 2.3 Venn Diagrams and Set Operations - Exercise Set 2.3 - Page 82: 98

$\{1,2,3,4,5,6,7,8\}$.

$B\cup C$ is the set of all numbers that are either a natural odd number and less than $9$ or a natural even number and less than $9$. Thus $B\cup C$ is the set of all numbers that are a natural number and less than $9$. Thus $B\cup C=\{1,2,3,4,5,6,7,8\}$.