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
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 2$. Sets of sets: Exercise $1$