Q.A universal set is given as $U = \{1, 2, 3, \dots, 10\}$. Let $A = \{2, 4, 6, 8, 10\}$ be the set of even numbers in $U$.

Check whether every element of $A$ lies in $U$ and whether the two sets are equal, then count each set and write $A$'s defining rule.

1. Subset check. Every element of $A$ — $2, 4, 6, 8, 10$ — is indeed in $U = \{1,\dots,10\}$, so $A \subseteq U$. Since $U$ also contains odd numbers ($1, 3, 5, 7, 9$) that are not in $A$, $A \ne U$; combined with $A \subseteq U$, this gives $A \subset U$ (a proper subset).
2. Cardinality. $A = \{2,4,6,8,10\}$ has 5 elements, so $n(A) = 5$. $U = \{1,2,\dots,10\}$ has 10 elements, so $n(U) = 10$. …