Exercises

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1. Truth tables — formula classification

(1) Is A∨¬A a tautology? — Try it

(2) Is (A→B)↔(¬B→¬A) a tautology? — Try it

(3) Does (A→B)∧(¬A→B) always have the same truth value as B? — Try it

(4) Modus tollens: A→B, ¬B ⊢ ¬A — Try it

(5) A→B, B ⊢ A — find a counterexample. — Try it

(6) What is the main connective of ∀x(Fx→∃yRxy)? — Try it

(7) What is the main connective of ¬(A∧B)∨C? — Try it

(8) ∀x(Fx→Gx), Fa ⊢ Ga — Try it

(9) ∃xFx ⊢ ∀xFx — find a countermodel. — Try it

(10) ∃x∀yRxy ⊢ ∀y∃xRxy — Try it

(11) A→B, B→C ⊢ A→C — Try it

(12) ∀x(Fx→Gx), ∀x(Gx→Hx) ⊢ ∀x(Fx→Hx) — Try it

(13) A→B, A→¬B ⊢ ¬A — Try it