Author: John Quintanilla

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.

Predicate Logic and Popular Culture (Part 4): A Streetcar Named Desire

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.

Let D(x,y,t) be the proposition “x depends on y at time t.” Translate the logical statement

\forall t \le 0 H(\hbox{I},\hbox{kindness of strangers},t),

where the domain is all times and time 0 is now.

The clunky way of translating this into English is, “For all times now and in the past, I depended on the kindness of strangers.” This was one of the American Film Institute’s Top 100 lines in the movies, from A Streetcar Named Desire.

 

Predicate Logic and Popular Culture (Part 3): Casablanca

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.

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

\forall t \ge 0 H(\hbox{We},\hbox{Paris},t),

where the domain is all times and time 0 is now.

The clunky way of translating this into English is, “For all times now and in the future, we will have Paris.” Of course, this sounds a whole lot better when Humphrey Bogart says it.

 

Predicate Logic and Popular Culture (Part 2)

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.

Let p be the proposition “You can write in the proper way,” let q be the proposition “You know how to conjugate,” and let r be the proposition “People mock you online.” Express the implication

\lnot (p \land q) \Longrightarrow r

in ordinary English.

By De Morgan’s Laws, the implication could also be written as

(\lnot p \lor \lnot q) \Longrightarrow r,

thus matching the opening two lines from Weird Al Yankovic’s Word Crimes (a parody of Robin Thicke’s Blurred Lines).

Predicate Logic and Popular Culture (Part 1)

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.

I’ll begin with a few simple examples to illustrate propositional logic.

Let p be the proposition “I am a crook.” Express the negation \lnot p in ordinary English.

Naturally, the negation is one of the most famous utterances in American political history.

Let p be the proposition “She’s cheer captain,” and let q be the proposition “I’m on the bleachers.” Express the conjunction

p \land q

in ordinary English.

I could have picked just about anything from popular culture to illustrate this idea, but my choice was Taylor Swift’s biggest hit as a country artist (before she switched to pop). The lyric in question is part of the song’s pre-chorus (for example, at the 39 second mark of the video below).

Let p be the proposition “I will get busy living,” and let q be the proposition “I will get busy dying.” Express the disjunction

p \lor q

in ordinary English.

Again, I could have picked almost anything to illustrate disjunctions. My choice comes from a famous scene from The Shawshank Redemption (at the 2:53 mark of the video below — warning, PG language in the rest of the video).

Let p be the proposition “You build it,” and let q be the proposition “He will come.” Express the implication

p \Longrightarrow q

in ordinary English.

Of course, this is the famous catchphrase from Field of Dreams.

One more for today:

Let p be the proposition “You want to roam,” and let q be the proposition “You roam.” Express the implication

p \Longrightarrow q

in ordinary English.

Though the order of the wording is different, this implication is part of the chorus of one of the biggest hits by the B-52s.