Remember Venn diagrams when you were in school?

Venn diagram showing what letter shapes are common in the Latin, Greek, and Cyrillic alphabets. By Watchduck (a.k.a. Tilman Piesk) (Own work) [Public domain], via Wikimedia Commons

John Venn wrote a paper in 1880 called *On the Diagrammatic and Mechanical Representation of Propositions and Reasonings* where he showed how to use these diagrams to demonstrate propositions and relationships. The overlapping areas show where elements of two or more sets are common to both or all of them. For example, we see from the above diagram that the characters O, A, B, E, M, X, K, Y, T, H, and P are common to to the Latin, Greek, and Cyrillic alphabets. That’s the triangular area where all three sets overlap, and is called the *intersection* of all three sets. In mathematical terms, if *L* is the Latin alphabet (upper right circle), *G* the Greek alphabet (upper left circle), and *C* is the Cyrillic alphabet (lower circle),

*L*∩

*G*∩

*C*= {O, A, B, E, M, X, K, Y, T, H, P}

There are other overlaps, like the section that has letters in both the Latin and Greek alphabets but not in Cyrillic:

*L*∩

*G*\

*C*= {I, N, Z}

Wikipedia, which regular readers will recall is the blogger’s best friend, has a whole article on Venn diagrams and what they all represent. My only purpose in talking about this is to say that the intersection of two or more sets is where they overlap.

from The Sound of One Hand Typing

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