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Home » Total used: \( 60 + 45 = 105 \) - Aurero

Total used: \( 60 + 45 = 105 \) - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 $ 0 \mid y $ nur fÃ¼r $ y = 0 $.

📌 $ y \mid 0 $: $ 0 \mid 0 $: wahr â Implikation wahr.

📌 $ x \mid 0 $: wahr â ganze Aussage wahr.

📌 Also: FÃ¼r **alle** $ x \in \mathbb{Z} $ ist $ x \mid 0 $ wahr, und da $ x \mid y \Rightarrow y \mid x $ fÃ¼r alle $ x \in \mathbb{Z} $ gilt **vergleichsweise begrenzt**, nÃ¤mlich fÃ¼r $ |x| \leq 1 $, und fÃ¼r $ |x| > 1 $ ist $ x \mid y \Rightarrow y \mid x $ falsz â $ P $ falsz â $ P \Rightarrow Q $ wahr.

📌 Aber ist $ x \mid y \Rightarrow y \mid x $ fÃ¼r **alle** $ x, y \in \mathbb{Z} $ wahr?

📌 Nein!** Gegenbeispiel: $ x = 2 $, $ y = 4 $: $ 2 \mid 4 $: wahr, $ 4 \mid 2 $? falsch â Implikation falsz.

📌 Also fÃ¼r $ x = 2 $, $ P $ falsz â $ P \Rightarrow Q $ wahr â Aussage wahr.

📌 Aber ist die gesamte Implikation $ orall x\, (P \Rightarrow Q) $ **echt wahr**?

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