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.φ

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]