 Consideration of the determinant-induced conditions on generalized consequence relations allows us incidentally to observe, somewhat surprisingly, that consequence relations (and the Set-Fmla framework) manage to distinguish the logics of any two truth-functions of the same arity. More precisely, suppose that f and g are distinct n-ary truth-functions, # is an n-ary connective, and Vf and Vg are the classes of valuations on which, respectively, f and g are associated with #; then the consequence relations determined by Vf and Vg are distinct. By way of illustration, suppose that n = 3 and f and g differ on some determinant beginning with T, F, F. (Thus we are considering the case in which the first component of a #-compound is true on a given valuation and the second and third are false.) Without loss of generality, we can assume that ⟨T, F, F, T⟩ ∈ f while ⟨T, F, F, F⟩ ∈ g. The conditions on a generalized consequence relation ⊩ induced by these determinants are respectively φ ⊩ ψ, χ, #(φ, ψ, χ) and φ, #(φ, ψ, χ) ⊩ ψ, χ. Thus in particular, taking φ as p and each of ψ, χ, as q, for the generalized consequence relation ⊩f, say, determined by Vf and that, ⊩g, determined by Vg, we have: