Exercise 4, § 3

Tag 03GC, permanent. Cite it as [Bourbaki, Tag 03GC].

Theory of Sets, I, 58

Let $A$ and $B$ be relations in a logical theory $\mathscr{T}$ . Let $A|B$ denote the relation "(not $A$ ) or (not $B$ )". Prove the following theorems in $\mathscr{T}$ :

(\text{not } A) \Leftrightarrow (A|A),

(A \text{ or } B) \Leftrightarrow ((A|A)|(B|B)),

(A \text{ and } B) \Leftrightarrow ((A|B)|(A|B)),

(A \Rightarrow B) \Leftrightarrow (A|(B|B)).

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