Wait â ist die Implikation also **immer wahr**?
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- $ (x \mid y \Rightarrow y \mid x) $ ist wahr, denn $ y \mid x $ und $ x \mid y $ both true.
- BUT: $ x \mid 0 $?
- $ x \mid 0 $ ist wahr für **jedes** $ x $, da $ 0 = 0 \cdot x $. So $ x \mid 0 $ gilt immer.
- Prämisse: $ orall y,\ (x \mid y \Rightarrow y \mid x) $ â ist dies für beliebige $ x $ wahr?
- Für $ x = 5 $: $ x \mid y \Rightarrow y \mid 5 $?
- Nehmen wir $ y = 10 $: $ 5 \mid 10 $: wahr. $ 10 \mid 5 $? Nein (10 ⤠5). Also Implikation falsch. â Prämisse falsch.
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