Introduction to Logic

Exercise 6.7 - Logical Entailment

Let Γ be a set of Relational Logic sentences, and let φ and ψ be individual Relational Logic sentences. For each of the following claims, state whether it is correct.

a. x.φ ⊨ φ
b. φ ⊨ ∀x
c. If Γ ⊨ ¬φ[τ] for some ground term τ, then Γ ⊭ ∀x.φ[x]
d. If Γ ⊨ φ[τ] for some ground term τ, then Γ ⊨ ∃x.φ[x]
e. If Γ ⊨ φ[τ] for every ground term τ, then Γ ⊨ ∀x.φ[x]