Set Theory/Examples/Unions and Intersections 2

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Examples in Set Theory

Let:

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


Then:

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


Sources