Disjoint Sets/Examples/3 Arbitrarily Chosen Sets
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Example of Disjoint 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.
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.1$: Sets and Subsets