Evaluation of Set Operations: Intersections and Unions

Given that \(\xi = \{x : x \text{ is an integer and}\hspace{0.5em} 10 \le x \le 20\}\),

\(M = \{x : x \text{ is a multiple of}\hspace{0.5em} 3\}\)

\(N = \{x : x \text{ is an even number} \} \)

1. List the elements of \(M \cap N\).
2. Find the value of \(k\) such that \(n(M \cap N) + k = n(M \cup N)\).

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