Predicate Logic and Popular Culture (Part 251): Animaniacs

“Survey Ladies” is one of the classics shorts from the 90s cartoon Animaniacs. While none of the survey questions can be stated in predicate logic (after all, they’re questions), there are many, many silly and somewhat repetitive statements that can be motivated by this cartoon:

Let $P$ be the set of all people, let $M(x)$ be the statement “ $x$ is watching a movie,” let $B(x)$ be the statement “ $x$ is eating beans,” and let $G(x)$ be the statement “ $x$ is with George Wendt.” Translate the following into symbolic logic:

Nobody is eating beans

Somebody is with George Wendt.

Somebody is not watching a movie.

Everyone watching a movie is eating beans.

Nobody watching a movie is with George Wendt.

Somebody is watching a movie but is not with George Wendt.

Nobody is both eating beans and is with George Wendt.

Everyone is watching a movie and is eating beans.

I’ll also share this for anyone who doesn’t remember the greatness of George Wendt:

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.

Predicate Logic and Popular Culture (Part 250): Marvin Gaye

Let $T$ be the set of all things, let $M(x)$ be the statement “ $x$ is a mountain,” let $V(x)$ be the statement “ $x$ is a valley,” let $R(x)$ be the statement “ $x$ is a river,” let $H(x)$ be the statement “ $x$ is high enough to keep me from getting to you, baby,” let $L(x)$ be the statement “ $x$ is low enough to keep me from getting to you, baby,” and let $W(x)$ be the statement “ $x$ is wide enough to keep me from getting to you, baby.” Translate the logical statement

$\sim \exists x \in T ((M(x) \land H(x)) \land (V(x) \land L(x)) \land (R(x) \land W(x)))$

This matches the chorus of the timeless “Ain’t No Mountain High Enough” by Marvin Gaye, which has increased in popularity in recent years thanks to the Marvel Cinematic Universe.

Predicate Logic and Popular Culture (Part 249): Billy Joel

Let $p$ be the statement “We started the fire,” let $q$ be the statement “We lit the fire,” and let $r$ be the statement “We tried to fight the fire.” Translate the logical statement

$\sim p \land \sim q \land r$

This matches part of the chorus of “We Didn’t Start the Fire” by Billy Joel.

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.