Set Theory: Intersections and Unions in a Finite Universal Set

Given that

\({\xi = \{x : x\text{ is an integer and}\hspace{0.5em} 1 \leq x \leq 15\}}\)

\({A = \{x : x\text{ is a prime number}\hspace{0.15em}\}}\)

\({B = \{x : x\text{ is a multiple of 3}\hspace{0.15em}\}}\)

\({C = \{x : \text{Exactly one digit of}\hspace{0.5em} x \text{ is}\hspace{0.5em} 1\}}\)

1. Write down the element in \(A \cap C\).
2. Find \(n(B \cup C)\).

All sets in this question are subsets of the stated universal set \(\xi\); every set-builder variable is restricted to that universe.