Yes, with the table you describe, participants in the A group would see two items: the first one in the definite Singular condition, the second one in the bare plural condition. Participants in the B group would see the same two items, but now the first one would be bare plural, and the second one definite Singular. The same logic extends to groups C, D and E.
Is that what you want?
Your table should also include columns for your other variable contents, so you probably want to add a Context column, a Question column and as many columns as there are different answer choices to that question on each trial (something like Answer1, Answer2, …)