295 Answers and Solutions to Selected Exercises Parsing tree: 3.1.7 (a) Formula: A = ¬∀x(x = 0) The set of subformulae: {A, ∀x(x = 0), x = 0} x=0 ∀x ¬ (main connective) (f) Formula: A = ¬∀x(¬x = 0) The main connective is ¬ The set of subformulae: {x = 0, ¬(x = 0), ∀x(¬x = 0), ¬∀x(¬x = 0)} The parsing tree: x=0 ¬ ∀ ¬ (j) Formula: A = ∀x((x < 0) → ∀x(x > 0)) Subformulae: {A, (x < 0) → ∀x(x > 0), ∀x(x > 0), x < 0, x > 0} Parsing tree: x>0 ∀x x