# Predicate Logic and Popular Culture (Part 40): Sesame Street

Let $L(x,y)$ be the proposition “$x$ is like $y$.” Translate the logical statement

$\exists x (\forall y(x \ne y \Longrightarrow \lnot L(x,y)) \land \forall y \forall z((x \ne y \land x \ne z) \Longrightarrow L(y,z)))$,

where the domain is all things being displayed.

The clunky way of translating this into English is, “There exists one thing that is not like all of the other things, and everything else besides that one thing is like everything else besides that one thing”… which has been learned by generations of American pre-schoolers on Sesame Street.

Context: Part of a discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent some time mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

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