Elementary Logic
Elementary Logic
Elementary Logic
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Relating the <strong>Logic</strong>al Connectives<br />
Lemma<br />
|= (A ↔ B) ↔ ((A → B) ∧ (B → A))<br />
|= (A → B) ↔ (¬A ∨ B)<br />
|= (A ∨ B) ↔ ¬(¬A ∧ ¬B)<br />
|= ⊥ ↔ (A ∧ ¬A)<br />
Note: these equivalences imply that some connectives could be<br />
dispensed with. We normally want a smaller set of connectives when<br />
analyzing properties of the logic and a larger set when actually using<br />
the logic.<br />
Yih-Kuen Tsay (SVVRL @ IM.NTU) <strong>Elementary</strong> <strong>Logic</strong> FLOLAC 2011 19 / 64
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