Intersection Distributes over Union/Examples/3 Arbitrarily Chosen Sets
Jump to navigation
Jump to search
Examples of Use of Intersection Distributes over Union
Let:
\(\ds A\) | \(=\) | \(\ds \set {3, -i, 4, 2 + i, 5}\) | ||||||||||||
\(\ds B\) | \(=\) | \(\ds \set {-i, 0, -1, 2 + i}\) | ||||||||||||
\(\ds C\) | \(=\) | \(\ds \set {- \sqrt 2 i, \dfrac 1 2, 3}\) |
Intersection with Union
\(\ds A \cap \paren {B \cup C}\) | \(=\) | \(\ds \set {3, -i, 4, 2 + i, 5} \cap \set {-i, 0, -\sqrt 2 i, -1, 2 + i, \dfrac 1 2, 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \set {3, -i, 2 + i}\) |
Union of Intersections
\(\ds \paren {A \cap B} \cup \paren {A \cap C}\) | \(=\) | \(\ds \set {-i, 2 + i} \cup \set 3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \set {3, -i, 2 + i}\) |
Thus it is seen that:
- $A \cap \paren {B \cup C} = \paren {A \cap B} \cup \paren {A \cap C}$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Solved Problems: Point Sets: $46$