## RWA Converse, Inverse, Contrapositive

### Topic

The mathematics in Alice in Wonderland

### Vocabulary

- Converse
- Inverse
- Contrapositive

### Student Exploration

#### They say mathematics is everywhere, but what about in fairy tales?

*Alice and Wonder Land* is an 1865 novel written by English author Charles Lutwidge Dodgson under the pseudonym Lewis Carroll, mathematician at Christ Church. It tells of a girl named Alice who falls down a rabbit hole into a fantasy world (Wonderland) populated by creatures.

The tale plays with logic, giving the story lasting popularity with adults as well as children. There are many references and mathematical concepts in both this story and *Through the Looking-Glass.*

For example in In chapter 7, “A Mad Tea-Party”, the March Hare, the Hatter, and the Dormouse give several examples in which the semantic value of a sentence **A** is not the same value of the converse of **A** (for example, “*Why, you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!”*); in logic and mathematics, this is discussing an inverse relationship. Read more at http://en.wikipedia.org/wiki/Alice%27s_Adventures_in_Wonderland

For more information go to http://www.maa.org/devlin/devlin_03_10.html

### Extension Investigation

Alice and Wonderland activity (see attachment)

### Resources Cited

http://en.wikipedia.org/wiki/Alice%27s_Adventures_in_Wonderland

http://www.maa.org/devlin/devlin_03_10.html