 For instance, regarding the issue of representing singular statements, they suggest to consider the Venn diagram circle as a representation of a set of things, and use first-order logic and set theory to treat categorical statements as statements about sets.Additionally, they propose to treat singular statements as statements about set membership.So, for example, to represent the statement "a is F" in this retooled Venn diagram, a small letter "a" may be placed inside the circle that represents the set F.

Venn diagrams correspond to truth tables for the propositions formula_5, formula_6, etc., in the sense that each region of Venn diagram corresponds to one row of the truth table.