Venn diagram with increasing numbers of sides. They are also two-dimensional representations of hypercubes. Henry John Stephen Smith devised similar "n"-set diagrams using sine curves with the series of equations Charles Lutwidge Dodgson (aka Lewis Carroll) devised a five-set diagram known as Carroll's square. Joaquin and Boyles, on the other hand, proposed supplemental rules for the standard Venn diagram in able to account for certain problem cases. 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
Skeffington Lutwidge the Navy, and is listed as a lieutenant in 1763, taking command of the purchased cutter in April that year. He remained with her until 1765, serving in the area of Liverpool. Lutwidge, by now a commander, commissioned the bomb vessel in June 1771, and served in the Irish Sea until the "Carcass" was paid off in April 1773. The "Carcass" was then refitted at Sheerness between March and April for a voyage to the Arctic, with Lutwidge retaining command. The expedition, under the overall command of Constantine Phipps, who commanded , sailed from the Nore on 10 June 1773.