Disjoint Sets/Examples

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Examples of Disjoint Sets

$3$ Arbitrarily Chosen Sets

Let:

\(\ds U\) \(=\) \(\ds \set {u_1, u_2, u_3}\)
\(\ds V\) \(=\) \(\ds \set {u_1, u_3}\)
\(\ds W\) \(=\) \(\ds \set {u_2, u_4}\)


Then:

\(\ds U \cup V\) \(=\) \(\ds \set {u_1, u_2, u_3}\)
\(\ds U \cap V\) \(=\) \(\ds \set {u_1, u_3}\)
\(\ds V \cup W\) \(=\) \(\ds \set {u_1, u_2, u_3, u_4}\)
\(\ds U \cap W\) \(=\) \(\ds \set {u_2}\)
\(\ds V \cap W\) \(=\) \(\ds \O\)

Thus $V$ and $W$ are disjoint.