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
Lewis Carroll his two sons were hardly more than babies. The older of these sons – yet another Charles Dodgson – was Carroll's father. He went to Westminster School and then to Christ Church, Oxford. He reverted to the other family tradition and took holy orders. He was mathematically gifted and won a double first degree, which could have been the prelude to a brilliant academic career. Instead, he married his first cousin Frances Jane Lutwidge in 1830 and became a country parson. Dodgson was born in the small parsonage at Daresbury in Cheshire near the towns of Warrington and Runcorn, the