Complement Math Example 1

Solution

1. 1
   The complement $A'$ (also written $A^c$ or $\bar{A}$) relative to universal set $U$ is defined as $A' = \{x \in U : x \notin A\}$.
2. 2
   List elements of $U = \{1,2,3,4,5,6,7,8,9,10\}$ that are not in $A = \{2,4,6,8,10\}$: remove the even numbers, leaving the odd numbers.
3. 3
   Therefore $A' = \{1,3,5,7,9\}$. Verify: $|A| + |A'| = 5 + 5 = 10 = |U|$ ✓.