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.

Predicate Logic and Popular Culture (Part 39): Taylor Swift

When teaching discrete mathematics, I’ll use today’s simple example to begin the section of propositional and predicate logic… it never fails to make my students chuckle.

Let $p$ be the proposition “We are getting back together.” Express the negation $\lnot p$ in ordinary English.

I’ll use this example to illustrate that the negation is simply “We are not getting back together,” without any need for extra emphasis or amplification… unlike the incredibly catchy Taylor Swift song.

Predicate Logic and Popular Culture (Part 38): The Blues Brothers

Let $N(x,y)$ be the proposition “ $x$ needs to love $y$ .” Translate the logical statement

$\forall x \exists y N(x,y)$ ,

where the domain is all people.

The clunky way of translating this into English is, “For every person, there exists a person who the first person needs to love.” But it sounds a lot better when sung by the Blues Brothers.

Predicate Logic and Popular Culture (Part 37): The Lord of the Rings

Let $L(x)$ be the proposition “ $x$ will love me,” and let $D(x)$ be the proposition “ $x$ will despair.” Translate the logical statement

$\forall x (L(x) \land D(x))$ ,

where the domain is all people.

This is one of the Galadriel’s predictions of the future had she accepted the One Ring from Frodo Baggins.

Predicate Logic and Popular Culture (Part 36): Hamlet

Let $R(x)$ be the proposition “ $x$ is rotten,” and let $D(x)$ be the proposition “ $x$ is in Denmark.” Translate the logical statement

$\exists x(R(x) \land D(x))$ ,

where the domain is all things.

The clunky way of translating this into English is, “There exists something that is rotten and in Denmark,” but the same thought is more dramatic when recited by it sounds better when recited by Marcellus at the start of Hamlet.

Predicate Logic and Popular Culture (Part 35): Elvis

Let $Y(x)$ be the proposition “You are $x$ .” Express the logical statement

$Y(\hbox{a hound dog}) \land \forall x(x \ne \hbox{a hound dog} \Rightarrow \lnot Y(x))$

into ordinary English, where the domain for $x$ are personal attributes.

Perhaps the shortest way to write this would be “You are only a hound dog,” but it’s much catchier when sung by Elvis.

Predicate Logic and Popular Culture (Part 34): The Beach Boys

Let $W(x,y)$ be the proposition “I wish that $x$ could be $y$ .” Translate the logical statement

$\forall x W(x, \hbox{a California girl})$

into plain English, where the domain for $x$ is all girls.

The simple way to translate this statement is “I wish that all girls could be California girls,” nearly matching the chorus of this classic by the Beach Boys.

Predicate Logic and Popular Culture (Part 33): The Eagles

Let $H(x,y,t)$ be the proposition “ $x$ hurts $y$ at time $t$ .” Translate the logical statement

$\exists x \exists y \exists t (0 \le t \le T \land H(x,y,t))$

into plain English, where the domain for $x$ and $y$ are all people, the domain for $t$ is all times, time $0$ is now, and time $T$ is when the night is through.

The simple way to translate this statement is “There are two people so that the first person will hurt the second person at some time between now and when the night is through.” A somewhat briefer way of expressing this thought is made in the first line of this popular song by The Eagles.

Predicate Logic and Popular Culture (Part 32): The Rolling Stones

Let $p$ be the proposition “I can get satisfaction.” Translate the logical statement $\lnot p$ into plain English.

The simple way to translate this statement is “I cannot get satisfaction.” The popular, though grammatically incorrect, way of expression this sentiment was made popular by the Rolling Stones.

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.

Predicate Logic and Popular Culture (Part 31): The Godfather

Let $p$ be the proposition “I took the gun,” and let $q$ be the proposition “I took the cannoli.” Translate the logical statement

$\lnot p \land q$ .

Obviously, this is an allusion to one of the great lines in The Godfather.

Even though this is a simple example, it actually serves a pedagogical purpose (when I first introduce students to propositional logic) by illustrating two important points.

First, there is an order of precedence with $\lnot$ and $\land$ . Specifically, $\lnot p \land q$ means $(\lnot p) \land q$ (“I did not take the gun, and I took the cannoli”) and not $\lnot (p \land q)$ (“It is false that I took both the gun and the cannoli”).

Second, the actual line from The Godfather is not a proposition because both “Leave the gun” and “Take the cannoli” are commands. By contrast, a proposition must be a declarative sentence that is either true or false. That’s why I had to slightly modify the words to “I took the cannoli” instead of “Take the cannoli.”

Context: This semester, I taught discrete mathematics for the first time. 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.

I’m afraid that I found plenty more examples from popular culture to illustrate predicate logic, but a month of posts on this topic is probably enough for now. I’ll return to this topic again at some point in the future.