Predicate Logic and Popular Culture (Part 57): Frozen

Let C(t) be the proposition “The cold bothers me at time t.” Translate the logical statement

\lnot(\exists t\le 0 (C(t))),

where the domain is all times and t=0 is now.

The straightforward way of translating this into English is, “It is false that there exists a time in the past that the cold bothered me.” Also, DeMorgan’s Laws could be applied:

\forall t\le 0(\lnot C(t)),

which can be read “For all times in the past, the cold did not bother me.” Of course, this is the closing line of the chorus of the signature tune from Frozen.

Of course, I can’t mention Frozen without mentioning its parodies; this is the best one that I’ve seen.

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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 56): The Byrds

Let S(x,t) be the proposition “t is the season for x.” Translate the logical statement

\forall x \exists t (S(x,t)).

This pretty much matches the opening line of the 1960s hit song by The Byrds from Ecclesiastes 3.

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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 55): The Quiet Man

Let L(x) be the proposition “x is a lock,” let B(x) be the proposition “x is a bolt,” and let H(x) be the proposition “x is in your own mercenary little heart.” Translate the logical statement

\forall x ( (L(x) \lor B(x)) \Rightarrow H(x)),

where the domain is all people.

The straightforward way of translating this into English is, “If it’s a lock or a bolt, then it’s in your own mercenary little heart.” With a little more emphasis, this is one of the great lines uttered by John Wayne in the 1952 film The Quiet Man (a wonderful movie which really needs to be digitized and restored to its original brilliance).

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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 54): Michael Jackson

Let p be the proposition “Billie Jean is my lover,” let q be the proposition “Billie Jean is a girl,” let r be the proposition “Billie Jean claims I am the one,” and let s be the proposition “The kid is my son.” Translate the logical statement \lnot p \land q \land r \land \lnot s.

Naturally, the translation is the chorus of one of Michael Jackson’s iconic hits.

See also the following rendition with bottles:

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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 53): Ylvis

Let G(x,y) be the proposition “x goes y.” Translate the logical statement

G(\hbox{dog},\hbox{woof}) \land G(\hbox{cat},\hbox{meow}) \land G(\hbox{bird}, \hbox{tweet}) \land G(\hbox{mouse}, \hbox{squeak})

\land G(\hbox{cow},\hbox{moo}) \land G(\hbox{frog}, \hbox{croak}) \land G(\hbox{elephant}, \hbox{toot})

\land G(\hbox{duck},\hbox{quack}) \land G(\hbox{fish},\hbox{blub}) \land G(\hbox{seal}, \hbox{ow ow ow})

With the slight exception of one line (“Ducks say quack”), this is the opening verse of perhaps the most head-scratching hit song in modern memory.

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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 52): Peabo Bryson

Let A(t) be the proposition “You are in my arms at time t,” and let H(x) be the proposition “I hold you at time t.” Translate the logical statement

(\exists t_1<0(A(t_1)) \land ( (\exists t_2>0 A(t_2)) \Rightarrow (\forall t \ge t_2(H(t))),

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

The straightforward way of translating this into English is, “There was a time in the past that you were in my arms, and if there exists a time that you are in my arms in the future, then I will hold you for all times after that.” More poetically, this is one of the lines of one of the great R&B love songs of the 1980s.

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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 51): Tears for Fears

Let L(x,t) be the proposition “x lasts until time t,” and let W(x) be the proposition “x wants to rule to world.” Translate the logical statement

\lnot (\exists x \forall t (L(x,t))) \land \forall x(W(x)),

where the domain is all people.

The straightforward way of translating this into English is, “It is false that there exists something that lasts for all time, and everybody wants to rule the world.” This matches the close of the second chorus of the 1980s hit song by Tears for Fears.

More recently, this song was covered by Lorde for the soundtrack of one of the Hunger Games movies.

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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 50): Brad Paisley

Let S(x,y) be the proposition “x sees y, and let T(x,y) be the proposition “x thinks y.” Translate the logical statement

(S(\hbox{you}, \hbox{deer}) \Rightarrow S(\hbox{you}, \hbox{Bambi}))

\land (S( \hbox{I}, \hbox{deer} ) \Rightarrow S( \hbox{I}, \hbox{antlers up on the wall}))

(S(\hbox{you}, \hbox{lake}) \Rightarrow T(\hbox{you}, \hbox{picnic}))

\land (S( \hbox{I}, \hbox{lake} ) \Rightarrow S( \hbox{I}, \hbox{a large mouth up under that log}))

This almost perfectly matches the opening two lines of Brad Paisley’s “I’m Still A Guy.”

And I can’t resist also showing a clip of Tim Tebow singing along to the chorus when Brad Paisley had a concert in Denver and Tebowmania was at an all-time high.

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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 49): Chris Janson

 

Let M(x) be the proposition “Money can buy me x.” Translate the logical statement

\lnot(\forall x (M(x))) \land M(\hbox{a boat}).

The straightforward way of translating this into English is, “It is false that money can buy me everything, and money can buy me a boat.” These are the closing lines of the chorus of the title song of Chris Janson’s debut country album.

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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 48): Jana Kramer

Let K(x,t) be the proposition “He kisses x at time t.” Translate the logical statement

\exists t_1 <0 (K(\hbox{I}, t_1) \land \forall t < t_1 \forall x( \lnot K(x,t)))

\land \exists t_2 <0 (K(\hbox{she}, t_2) \land \forall t > t_2 \forall x( \lnot K(x,t))) ,

where time 0 is now.

The straightforward way of translating this into English is, “There was a time in the past that he kissed me, and no one kissed him before then; and there will be a time in the future that he’ll kiss her, and no one will kiss him after that.” More succinctly, this is the first line of the chorus of one of country music’s biggest hits from 2015.

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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.