 The implication from (i) to the conclusion that ⊢ ⊇ ⊢CL has been stressed in several publications by S. Pollard (Pollard 2002, Pollard and Martin 1996); there is a similar proof for the implication from (ii). Neither proof is given here—only an illustration (of case (ii)). The truth-function known as exclusive disjunction (or xor), which differs from that associated on Boolean valuations with ∨ (“inclusive disjunction”) by having ⟨T, T, F⟩ instead of the determinant ⟨T, T, T⟩, will serve as an example, since as well as the determinant just mentioned, which has T’s except for the final F, we have a T-final determinant (e.g.) ⟨T, F, T⟩. The induced conditions on generalized consequence relations for these two determinants are respectively: