# Predicate Logic and Popular Culture (Part 248): The Fellowship of the Ring

Let $T$ be the set of all things, let $P$ be the set of all people, let $G(x)$ be the statement “$x$ is made of gold,” let $B(x)$ be the statement “$x$ glitters,” let $W(x)$ be the statement “$x$ wanders,” and let $L(x)$ be the statement “$x$ is lost.” Translate the logical statement

$\sim \forall x \in T(G(x) \Longrightarrow B(x)) \land \sim \forall x \in P(W(x) \Longrightarrow L(x))$

This matches the opening two lines of the poem “All That Is Gold Does Not Glitter” in the book The Fellowship of the Ring.

Context: Part of the 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 a few days 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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