2.5.9: Derivability and the Propositional Connectives
- \(A \lor B, \lnot A, \lnot B\) is inconsistent.
- Both \(A \Proves A \lor B\) and \(B \Proves A \lor B\) .
Proof.
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Consider the following derivation:
This is a derivation of \(\lfalse\) from undischarged assumptions \(A \lor B\) , \(\lnot A\) , and \(\lnot B\) .
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We can derive both
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