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6 Exercises Propositional Logic

Exercise 1 One can give the truth table for Boolean formulae in a similar way as the Semantic Boolean operators, i.e., for ∧ :

 tru e  true  |true
 tru e  false |fa lse
 false  true  |fa lse
 false  false  fa lse

Give the truth table for the following Boolean formulae:

(p) ∨ (q ∧ r)
(p) ≡ (q ∨ r)

Exercise 2 Let σ (p) = tt
 0  and σ (q) = tt
 0  .

Give the semantics of p ≡ q , i.e., calculate ⟦p ≡  q⟧
      σ0  .

Exercise 3 Show that for any state σ0  and for propositional variables p and q the following holds ⟦p ∨ q⟧σ0 = (⟦p ⟧σ0 or⟦q⟧σ0) .