Predicate Logic and Popular Culture (Part 86): My Fair Lady

Let $T(t)$ be the proposition “ $t$ is at night” and let $D(t)$ be the proposition “I could have danced at time $t$ .” Translate the logical statement

$\forall t (T(t) \Rightarrow D(t))$ .

This needs no further introduction:

I also really enjoyed this (she made the finals of Britain’s Got Talent in 2009):

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.

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 85): Three Dog Night

Let $p$ be the proposition “Jeremiah was a bullfrog,” let $q$ be the proposition “Jeremiah was a good friend of mine,” let $W(x)$ be the proposition “ $x$ is a word,” let $S(x,t)$ be the proposition “Jeremiah said $x$ at time $t$ ,” let $U(x,t)$ be the proposition “I understood $x$ at time $t$ ,” let $r$ be the proposition “I helped Jeremiah drink his wine,” let $W(x)$ be the proposition “ $x$ is mighty fine wine,” and let $J(x,t)$ be the proposition “Jeremiah had $x$ at time $t$ .” Translate the logical statement

$p \land q \land \forall x \forall t<0(W(x) \land S(x,t) \Rightarrow \lnot U(x,t)) \land r \land \forall t<0 \exists x(W(x) \land J(x,t))$ ,

where time 0 is now.

Of course, this matches the opening verse of one of the classics of the 1970s.

Predicate Logic and Popular Culture (Part 84): OMD

Let $F(s,t)$ be the proposition “You said at time $s$ that we’d still be friends at time $t$ .” Translate the logical statement

$\forall s<0 \exists t>0 F(s,t)$ .

This matches the last line of the first chorus from “If You Leave.”

For what it’s worth, this was the opening song on the Pretty in Pink soundtrack, which remains for my money the best movie soundtrack ever made.

Predicate Logic and Popular Culture (Part 83): The Sound of Music

Let $C(x,y)$ be the proposition “ $x$ comes from $y$ ,” let $Y(t)$ be the proposition “ $t$ is in my youth or childhood,” let $D(x,t)$ be the proposition “I did $x$ at time $t$ ,” and let $G(x)$ be the proposition “ $x$ is good.” Translate the logical statement

$(\lnot \exists x \forall y \lnot C(x,y)) \Rightarrow \exists x \exists t(Y(t) \land G(x) \land D(x,t))$ .

The straightforward English translation is, “If it’s false that something can come from nothing, then there exists something good that I did in my youth or childhood.” More poetically, it’s the chorus of the great song that Captain Von Trapp and Maria sang before they got married in The Sound of Music.

See also the version with Carrie Underwood from the NBC live special:

Predicate Logic and Popular Culture (Part 82): ZZ Top

Let $G(x)$ be the proposition “ $x$ is a girl,” and let $S(x)$ be the proposition “ $x$ is crazy about a sharp-dressed man.” Translate the logical statement

$\forall x (G(x) \Rightarrow S(x))$ .

I don’t think this one needs any further introduction:

Predicate Logic and Popular Culture (Part 81): My Fair Lady

Let $D(x)$ be the proposition “ $x$ is a duke,” let $E(x)$ be the proposition “ $x$ is an earl,” let $P(x)$ be the proposition “ $x$ is a peer”, and let $H(x)$ be the proposition “ $x$ is here.” Translate the logical statement

$\forall x ((D(x) \lor E(x) \lor P(x)) \Rightarrow H(x))$ .

This matches the opening line of “Ascot Gavotte” from My Fair Lady.

Predicate Logic and Popular Culture (Part 80): Liverpool FC

Let $W(x,t)$ be the proposition “You walk with $x$ at time $t$ .” Translate the logical statement

$\lnot \exists t \forall x \lnot W(x,t)$ .

The straightforward way of translating this into English is, “It’s false that there exists a time that you will walk with nobody.” Using DeMorgan’s Laws, this can be rewritten as

$\forall t \exists x W(x,t)$ ,

or “At all times, you’ll walk with somebody.”

Nevertheless, the more complicated version matches the anthem of Liverpool FC.

For a more traditional arrangement:

Predicate Logic and Popular Culture (Part 79): Twister Sister

Let $T(t)$ be the proposition “We are going to take it at time $t$ .” Translate the logical statement

$\forall t (\lnot T(t))$ .

Naturally, this matches one of the great heavy metal songs of the 1980s.

Predicate Logic and Popular Culture (Part 78): Starship

Let $B(t)$ be the proposition “We can build this dream together standing strong at time $t$ ,” and let $S(x)$ be the proposition “ $x$ can stop us now.” Translate the logical statement

$(\forall t \ge 0 B(t)) \land \lnot (\exists x S(x))$ .

Of course, this is the first half of the chorus of the Starship classic.

Predicate Logic and Popular Culture (Part 77): Don Henley

Let $W(x)$ be the proposition “She wants to do $x$ .” Translate the logical statement

$W(\hbox{dance}) \land \forall x (x \ne \hbox{dance} \Rightarrow \lnot W(x))$ .

The straightforward way of translating this into English is, “She wants to dance, and if something is dancing, then she doesn’t want to do that.” This approximately matches the sentiment of this 1980s classic.