Set Union/Examples

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Examples of Set Union

Example: $2$ Arbitrarily Chosen Sets

Let:

\(\displaystyle S\) \(=\) \(\displaystyle \set {a, b, c}\) $\quad$ $\quad$
\(\displaystyle T\) \(=\) \(\displaystyle \set {c, e, f, b}\) $\quad$ $\quad$

Then:

$S \cup T = \set {a, b, c, e, f}$


Example: $3$ Arbitrarily Chosen Sets

Let:

\(\displaystyle A_1\) \(=\) \(\displaystyle \set {1, 2, 3, 4}\) $\quad$ $\quad$
\(\displaystyle A_2\) \(=\) \(\displaystyle \set {1, 2, 5}\) $\quad$ $\quad$
\(\displaystyle A_3\) \(=\) \(\displaystyle \set {2, 4, 6, 8, 12}\) $\quad$ $\quad$

Then:

$A_1 \cup A_2 \cup A_3 = \set {1, 2, 3, 4, 5, 6, 8, 12}$


Example: People who are Blue-Eyed or British

Let:

\(\displaystyle B\) \(=\) \(\displaystyle \set {\text {British people} }\) $\quad$ $\quad$
\(\displaystyle C\) \(=\) \(\displaystyle \set {\text {Blue-eyed people} }\) $\quad$ $\quad$

Then:

$B \cup C = \set {\text {People who are blue-eyed or British or both} }$


Example: Overlapping Integer Sets

Let:

\(\displaystyle A\) \(=\) \(\displaystyle \set {x \in \Z: 2 \le x}\) $\quad$ $\quad$
\(\displaystyle B\) \(=\) \(\displaystyle \set {x \in \Z: x \le 5}\) $\quad$ $\quad$

Then:

$A \cap B = \Z$