Identify the Universal Set and Subset

We are given the universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and the subset $A = \{1, 3, 5, 7, 9\}$.

$U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}, \quad A = \{1, 3, 5, 7, 9\}$

Apply the Complement Formula

The complement of set $A$ is defined as the set of all elements in $U$ that are not in $A$, given by $A' = U \setminus A$.

$A' = U \setminus A$

Compute the Complement Set

Removing the elements of $A$ from $U$, we obtain the set $A' = \{2, 4, 6, 8, 10\}$.

$A' = \{2, 4, 6, 8, 10\}$

Determine the Cardinality

Counting the elements in $A'$, we find a total of $5$ elements, which corresponds to Option B.

$n(A') = 5$