Öffnen – Leere Lösungsmenge – Aufgaben (PDF)
Leere Lösungsmenge
Eine leere Menge ist eine Menge, die keine Elemente enthält. Die leere Menge wird auch als Null-Menge oder als Nullstelle bezeichnet. Im Bereich der Mengenlehre ist die leere Menge ein axiomatischer Begriff und wird mit dem Zeichen ∅ (Umschrift: phi) bezeichnet.
Beispiel 1:
Gegeben ist die Menge A = {1, 2, 3, 4}. Suchen Sie nach allen Teilmengen von A, die genau 2 Elemente enthalten.
Lösung:
Die Menge A hat die folgenden Teilmengen mit 2 Elementen: {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4} und {3, 4}.
Beispiel 2:
Gegeben ist die Menge B = x ist eine natürliche Zahl und x < 10. Finden Sie alle Teilmengen von B.
Lösung:
Die Menge B hat die folgenden Teilmengen: {0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {0, 1}, {0, 2}, {0, 3}, {0, 4}, {0, 5}, {0, 6}, {0, 7}, {0, 8}, {0, 9}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7}, {1, 8}, {1, 9}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 7}, {2, 8}, {2, 9}, {3, 4}, {3, 5}, {3, 6}, {3, 7}, {3, 8}, {3, 9}, {4, 5}, {4, 6}, {4, 7}, {4, 8}, {4, 9}, {5, 6}, {5, 7}, {5, 8}, {5, 9}, {6, 7}, {6, 8}, {6, 9}, {7, 8}, {7, 9}, {8, 9}, {0, 1, 2}, {0, 1, 3}, {0, 1, 4}, {0, 1, 5}, {0, 1, 6}, {0, 1, 7}, {0, 1, 8}, {0, 1, 9}, {0, 2, 3}, {0, 2, 4}, {0, 2, 5}, {0, 2, 6}, {0, 2, 7}, {0, 2, 8}, {0, 2, 9}, {0, 3, 4}, {0, 3, 5}, {0, 3, 6}, {0, 3, 7}, {0, 3, 8}, {0, 3, 9}, {0, 4, 5}, {0, 4, 6}, {0, 4, 7}, {0, 4, 8}, {0, 4, 9}, {0, 5, 6}, {0, 5, 7}, {0, 5, 8}, {0, 5, 9}, {0, 6, 7}, {0, 6, 8}, {0, 6, 9}, {0, 7, 8}, {0, 7, 9}, {0, 8, 9}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 2, 6}, {1, 2, 7}, {1, 2, 8}, {1, 2, 9}, {1, 3, 4}, {1, 3, 5}, {1, 3, 6}, {1, 3, 7}, {1, 3, 8}, {1, 3, 9}, {1, 4, 5}, {1, 4, 6}, {1, 4, 7}, {1, 4, 8}, {1, 4, 9}, {1, 5, 6}, {1, 5, 7}, {1, 5, 8}, {1, 5, 9}, {1, 6, 7}, {1, 6, 8}, {1, 6, 9}, {1, 7, 8}, {1, 7, 9}, {1, 8, 9}, {2, 3, 4}, {2, 3, 5}, {2, 3, 6}, {2, 3, 7}, {2, 3, 8}, {2, 3, 9}, {2, 4, 5}, {2, 4, 6}, {2, 4, 7}, {2, 4, 8}, {2, 4, 9}, {2, 5, 6}, {2, 5, 7}, {2, 5, 8}, {2, 5, 9}, {2, 6, 7}, {2, 6, 8}, {2, 6, 9}, {2, 7, 8}, {2, 7, 9}, {2, 8, 9}, {3, 4, 5}, {3, 4, 6}, {3, 4, 7}, {3, 4, 8}, {3, 4, 9}, {3, 5, 6}, {3, 5, 7}, {3, 5, 8}, {3, 5, 9}, {3, 6, 7}, {3, 6, 8}, {3, 6, 9}, {3, 7, 8}, {3, 7, 9}, {3, 8, 9}, {4, 5, 6}, {4, 5, 7}, {4, 5, 8}, {4, 5, 9}, {4, 6, 7}, {4, 6, 8}, {4, 6, 9}, {4, 7, 8}, {4, 7, 9}, {4, 8, 9}, {5, 6, 7}, {5, 6, 8}, {5, 6, 9}, {5, 7, 8}, {5, 7, 9}, {5, 8, 9}, {6, 7, 8}, {6, 7, 9}, {6, 8, 9}, {7, 8, 9}, {0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 2, 5}, {0, 1, 2, 6}, {0, 1, 2, 7}, {0, 1, 2, 8}, {0, 1, 2, 9}, {0, 1, 3, 4}, {0, 1, 3, 5}, {0, 1, 3, 6}, {0, 1, 3, 7}, {0, 1, 3, 8}, {0, 1, 3, 9}, {0, 1, 4, 5}, {0, 1, 4, 6}, {0, 1, 4, 7}, {0, 1, 4, 8}, {0, 1, 4, 9}, {0, 1, 5, 6}, {0, 1, 5, 7}, {0, 1, 5, 8}, {0, 1, 5, 9}, {0, 1, 6, 7}, {0, 1, 6, 8}, {0, 1, 6, 9}, {0, 1, 7, 8}, {0, 1, 7, 9}, {0, 1, 8, 9}, {0, 2, 3, 4}, {0, 2, 3, 5}, {0, 2, 3, 6}, {0, 2, 3, 7}, {0, 2, 3, 8}, {0, 2, 3, 9}, {0, 2, 4, 5}, {0, 2, 4, 6}, {0, 2, 4, 7}, {0, 2, 4, 8}, {0, 2, 4, 9}, {0, 2, 5, 6}, {0, 2, 5, 7}, {0, 2, 5, 8}, {0, 2, 5, 9}, {0, 2, 6, 7}, {0, 2, 6, 8}, {0, 2, 6, 9}, {0, 2, 7, 8}, {0, 2, 7, 9}, {0, 2, 8, 9}, {0, 3, 4, 5}, {0, 3, 4, 6}, {0, 3, 4, 7}, {0, 3, 4, 8}, {0, 3, 4, 9}, {0, 3, 5, 6}, {0, 3, 5, 7}, {0, 3, 5, 8}, {0, 3, 5, 9}, {0, 3, 6, 7}, {0, 3, 6, 8}, {0, 3, 6, 9}, {0, 3, 7, 8}, {0, 3, 7, 9}, {0, 3, 8, 9}, {0, 4, 5, 6}, {0, 4, 5, 7}, {0, 4, 5, 8}, {0, 4, 5, 9}, {0, 4, 6, 7}, {0, 4, 6, 8}, {0, 4, 6, 9}, {0, 4, 7, 8}, {0, 4, 7, 9}, {0, 4, 8, 9}, {0, 5, 6, 7}, {0, 5, 6, 8}, {0, 5, 6, 9}, {0, 5, 7, 8}, {0, 5, 7, 9}, {0, 5, 8, 9}, {0, 6, 7, 8}, {0, 6, 7, 9}, {0, 6, 8, 9}, {0, 7, 8, 9}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, {1, 2, 3, 7}, {1, 2, 3, 8}, {1, 2, 3, 9}, {1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 4, 7}, {1, 2, 4, 8}, {1, 2, 4, 9}, {1, 2, 5, 6}, {1, 2, 5, 7}, {1, 2, 5, 8}, {1, 2, 5, 9}, {1, 2, 6, 7}, {1, 2, 6, 8}, {1, 2, 6, 9}, {1, 2, 7, 8}, {1, 2, 7, 9}, {1, 2, 8, 9}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 4, 7}, {1, 3, 4, 8}, {1, 3, 4, 9}, {1, 3, 5, 6}, {1, 3, 5, 7}, {1, 3, 5, 8}, {1, 3, 5, 9}, {1, 3, 6, 7}, {1, 3, 6, 8}, {1, 3, 6, 9}, {1, 3, 7, 8}, {1, 3, 7, 9}, {1, 3, 8, 9}, {1, 4, 5, 6}, {1, 4, 5, 7}, {1, 4, 5, 8}, {1, 4, 5, 9}, {1, 4, 6, 7}, {1, 4, 6, 8}, {1, 4, 6, 9}, {1, 4, 7, 8}, {1, 4, 7, 9}, {1, 4, 8, 9}, {1, 5, 6, 7}, {1, 5, 6, 8}, {1, 5, 6, 9}, {1, 5, 7, 8}, {1, 5, 7, 9}, {1, 5, 8, 9}, {1, 6, 7, 8}, {1, 6, 7, 9}, {1, 6, 8, 9}, {1, 7, 8, 9}, {2, 3, 4, 5}, {2, 3, 4, 6}, {2, 3, 4, 7}, {2, 3, 4, 8}, {2, 3, 4, 9}, {2, 3, 5, 6}, {2, 3, 5, 7}, {2, 3, 5, 8}, {2, 3, 5, 9}, {2, 3, 6, 7}, {2, 3, 6, 8}, {2, 3, 6, 9}, {2, 3, 7, 8}, {2, 3, 7, 9}, {2, 3, 8, 9}, {2, 4, 5, 6}, {2, 4, 5, 7}, {2, 4, 5, 8}, {2, 4, 5, 9}, {2, 4, 6, 7}, {2, 4, 6, 8}, {2, 4, 6, 9}, {2, 4, 7, 8}, {2, 4, 7, 9}, {2, 4, 8, 9}, {2, 5, 6, 7}, {2, 5, 6, 8}, {2, 5, 6, 9}, {2, 5, 7, 8}, {2, 5, 7, 9}, {2, 5, 8, 9}, {2, 6, 7, 8}, {2, 6, 7, 9}, {2, 6, 8, 9}, {2, 7, 8, 9}, {3, 4, 5, 6}, {3, 4, 5, 7}, {3, 4, 5, 8}, {3, 4, 5, 9}, {3, 4, 6, 7}, {3, 4, 6, 8}, {3, 4, 6, 9}, {3, 4, 7, 8}, {3, 4, 7, 9}, {3, 4, 8, 9}, {3, 5, 6, 7}, {3, 5, 6, 8}, {3, 5, 6, 9}, {3, 5, 7, 8}, {3, 5, 7, 9}, {3, 5, 8, 9}, {3, 6, 7, 8}, {3, 6, 7, 9}, {3, 6, 8, 9}, {3, 7, 8, 9}, {4, 5, 6, 7}, {4, 5, 6, 8}, {4, 5, 6, 9}, {4, 5, 7, 8}, {4, 5, 7, 9}, {4, 5, 8, 9}, {4, 6, 7, 8}, {4, 6, 7, 9}, {4, 6, 8, 9}, {4, 7, 8, 9}, {5, 6, 7, 8}, {5, 6, 7, 9}, {5, 6, 8, 9}, {5, 7, 8, 9}, {6, 7, 8, 9}, {0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 3, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 3, 9}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 4, 7}, {0, 1, 2, 4, 8}, {0, 1, 2, 4, 9}, {0, 1, 2, 5, 6}, {0, 1, 2, 5, 7}, {0, 1, 2, 5, 8}, {0, 1, 2, 5
Öffnen – Leere Lösungsmenge – Übungen (PDF)
