Complement Math Example 2

Solution

1. 1
   Work from the inside out. First find $A \cap B$: elements in both $A = \{1,2,3,4,5\}$ and $B = \{4,5,6,7\}$ are $\{4,5\}$.
2. 2
   Now take the complement of $\{4,5\}$ relative to $U = \{1,2,3,4,5,6,7,8,9,10\}$: remove 4 and 5 from $U$.
3. 3
   $(A \cap B)' = \{1,2,3,6,7,8,9,10\}$. By De Morgan's law this also equals $A' \cup B'$; verify: $A' = \{6,7,8,9,10\}$, $B' = \{1,2,3,8,9,10\}$, and their union is $\{1,2,3,6,7,8,9,10\}$ ✓.