**1.** *Let us first define:* The set of propositional formulae of, say, set theory, denoted here by **Prop**, is the smallest set such that

(1) Every Boolean variable is in **Prop** (cf. 1.1.1.26)

(2) If and are in **Prop**, then so are (¬) and () —where I used as an abbreviation of any member of {⋀, ⋁, →, ≡}.

If we call **WFF** the set of all formulae of set theory as defined in 1.1.1.3, then show that **WFF** = **Prop**.

*Hint.* This involves two structural inductions, one each over **WFF** and **Prop**.

**2.** Prove the general case of proof by cases (cf. 1.1.1.48): → , → ⊢ ⋁ → ⋁ .

**3.** Let us prove ...

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