Foundations of Set Theory: Union and Universal Operations

\(\xi = \{x : x \text{ is an integer and}\hspace{0.5em} 1 \le x < 10\}\)

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

\(R = \{x : x \text{ is a perfect square}\hspace{0.15em}\}\)

\(S = \{x : x \text{ is a multiple of ~} 3\}\)

1. List the elements in the set \(R \cup S\).
2. List the elements in the set \(P \cup S\).

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