Set Theory/Examples/Unions and Intersections 2

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Examples in Set Theory

Let:

\(\displaystyle A\) \(=\) \(\displaystyle \set {1, 2}\)
\(\displaystyle B\) \(=\) \(\displaystyle \set {1, \set 2}\)
\(\displaystyle C\) \(=\) \(\displaystyle \set {\set 1, \set 2}\)
\(\displaystyle D\) \(=\) \(\displaystyle \set {\set 1, \set 2, \set {1, 2} }\)


Then:

\(\displaystyle A \cap B\) \(=\) \(\displaystyle \set 1\)
\(\displaystyle \paren {B \cap D} \cup A\) \(=\) \(\displaystyle \set {1, 2, \set 2}\)
\(\displaystyle \paren {A \cap B} \cup D\) \(=\) \(\displaystyle \set {1, \set 1, \set 2, \set {1, 2} }\)
\(\displaystyle \paren {A \cap B} \cup \paren {C \cap D}\) \(=\) \(\displaystyle \set {1, \set 1, \set 2}\)


Sources