Set Theory/Examples/Unions and Intersections 1

From ProofWiki
Jump to navigation Jump to search

Example in Set Theory

Let:

\(\displaystyle V_1\) \(=\) \(\displaystyle \set {v_1, v_3, v_4}\)
\(\displaystyle V_2\) \(=\) \(\displaystyle \set {v_2, v_5}\)
\(\displaystyle V_3\) \(=\) \(\displaystyle \set {v_1, v_3}\)


Then:

\(\displaystyle V_1 \cup V_2\) \(=\) \(\displaystyle \set {v_1, v_2, v_3, v_4, v_5}\)
\(\displaystyle V_1 \cup V_3\) \(=\) \(\displaystyle \set {v_1, v_3, v_4}\)
\(\displaystyle V_2 \cup V_3\) \(=\) \(\displaystyle \set {v_1, v_2, v_3, v_5}\)
\(\displaystyle V_1 \cap V_2\) \(=\) \(\displaystyle \O\)
\(\displaystyle V_1 \cap V_3\) \(=\) \(\displaystyle \set {v_1, v_3}\)
\(\displaystyle V_2 \cap V_3\) \(=\) \(\displaystyle \O\)


Thus:

$V_1$ and $V_2$ are disjoint
$V_2$ and $V_3$ are disjoint.


Sources