Intersection Distributes over Union/Examples/3 Arbitrarily Chosen Sets/Union of Intersections

Examples of Use of Intersection Distributes over Union

Let:

\(\ds A\)

\(=\)

\(\ds \set {3, -i, 4, 2 + i, 5}\)

\(\ds B\)

\(=\)

\(\ds \set {-i, 0, -1, 2 + i}\)

\(\ds C\)

\(=\)

\(\ds \set {-\sqrt 2 i, \dfrac 1 2, 3}\)

Then:

\(\ds \paren {A \cap B} \cup \paren {A \cap C}\)

\(=\)

\(\ds \set {-i, 2 + i} \cup \set 3\)

\(\ds \)

\(=\)

\(\ds \set {3, -i, 2 + i}\)

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Solved Problems: Point Sets: $46 \ \text {(e)}$