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
Charles Dodgson (priest) at Preston Brook, and held weekly services there for the bargees. In 1843 Dodgson was given the Crown living of Croft, Yorkshire, by the Prime Minister, Robert Peel, at the urging of Longley. In 1852 he was additionally collated as a canon of Ripon Cathedral and in 1854 became the Archdeacon of Richmond. At Croft he restored the chancel of St Peter's Church and once again started a school, sacrificing part of the glebe to it. He taught there, as did his wife and later some of his children. Dodgson was a contemporary and college friend of Edward Bouverie Pusey,