Lineare Algebra Beispiele

A = (1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19)

$A = (1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19)$ ,

b = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)

$b = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)$

Schritt 1

Gib die Darstellung der Schnittmenge der Mengen

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

${1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}$ und

{1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}

${1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}$ wieder.

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} \cap {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}

${1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} \cap {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}$

Schritt 2

Die Schnittmenge zweier Mengen ist die Menge aller Elemente, die in beiden Mengen enthalten ist.

{1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}

${1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}$

Schritt 3

Die Komplementärmenge der beiden Mengen sind die verbleibenden Elemente von

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

${1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}$ , die keine Elemente der Schnittmenge der beiden Mengen sind.

{2, 4, 8, 10, 14, 16, 20}

${2, 4, 8, 10, 14, 16, 20}$