Why are the following not propositional formulae? There might be more than one reason
As seen in the course notes false,f1 ∨ f2,f1 ⊃ f2 and f1 ≡ f2 are derived propositional formulae.
Write out ((P ∨ Q) ∧ (Q ⊃ P)) using only ¬and ∧.
Give the truth table for the following propositional formulae:
Let σ0(P) = tt and σ0(Q) = tt.
Give the semantics of P ≡ Q, i.e., calculate M⟦P ≡ Q⟧(σ0).
Show that for any state σ0 and for propositional variables P and Q the following holds M⟦P ∨ Q⟧(σ0) = (M⟦P⟧(σ0) or M⟦Q⟧(σ0)).
Let P, Q, and R be propositional variables capturing the following propositions:
Write the following as formulae using P, Q, and R and logical connectives.
Determine which of the following formula is satisfiable or valid. Explain why.