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Asks the student whether a map between two finite sets, given schematically \"by arrows\" is injective/surjective/bijective.

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Gegeben ist die folgende Abbildung $\\{1, \\dots, \\var{card_x}\\}$$\\{ 1\\}$ $\\to$ $\\{ 1, \\dots, \\var{card_y}\\}$$\\{1\\}$:

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{vector_plot()}

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Welche der folgenden Eigenschaften hat die oben dargestelle Abbildung?

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Erinnern Sie sich an die Definitionen:

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Eine Abbildung $f$ heißt injektiv, wenn für alle $x$, $x'$ im Definitionsbereich mit $x\\ne x'$ gilt: $f(x)\\ne f(x')$. Für die Darstellung einer Abbildung mit Pfeilen, wie sie hier gegeben ist, bedeutet das: es dürfen nicht zwei verschiedene Pfeile den selben Zielpunkt haben.

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Eine Abbildung $f$ heißt surjektiv, wenn zu jedem Element $y$ des Zielbereichs ein Element $x$ im Definitionsbereich mit $f(x)=y$ existiert. Für die Darstellung einer Abbildung mit Pfeilen, wie sie hier gegeben ist, bedeutet das: An jedem Punkt des Zielbereichs (hier auf der rechten Seite) muss ein Pfeil enden.

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Eine Abbildung heißt bijektiv, wenn sie sowohl injektiv als auch surjektiv ist.

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