Disjoint Sets/Examples/3 Arbitrarily Chosen Sets

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Example of Disjoint Sets

Let:

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


Then:

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

Thus $V$ and $W$ are disjoint.


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