GF(2)-grammars are a recently introduced grammar family that has some unusual algebraic properties and is closely connected to the family of unambiguous grammars. By using the method of formal power series, we establish strong conditions that are necessary for subsets of a1∗a2∗⋯ak∗ to be described by some GF(2)-grammar. By further applying the established results, we settle the long-standing open question of proving the inherent ambiguity of the language {anbmcℓ∣n≠morm≠ℓ}, as well as give a new, purely algebraic, proof of the inherent ambiguity of the language {anbmcℓ∣n=morm=ℓ}.