Predicate Logic and Popular Culture (Part 166): Ed Sheeran

Let T be the set of all things, let S(x) be the proposition “I see x,” and let F(x) be the proposition “I have faith in x.” Translate the logical statement

\forall x \in T (S(x) \Rightarrow F(x)).

This is one of lines from the recent smash hit by Ed Sheeran.

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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 165): Eleanor Roosevelt

Let P be the set of all people, let C(x) be the proposition “You consent to let x make you feel inferior,” and let F(x) be the proposition “x makes you feel inferior.” Translate the logical statement

\forall x \in P (F(x) \Rightarrow C(x)).

This is the contrapositive of a famous quote by Eleanor Roosevelt.

Source: https://www.brainyquote.com/quotes/eleanor_roosevelt_161321

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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 164): Kenny Chesney

Let H be the set of all things, let T be the set of all times, let S(t) be the proposition “The sun goes down at time t,” and let H(x,t) be the temperature of x at time $t$.” Translate the logical statement

\forall t \in T (S(t) \Rightarrow \forall x \in H( \displaystyle \frac{\partial H}{\partial t}(x,t) > 0)).

This matches the chorus from a popular country song by Kenny Chesney.

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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 163): The Princess Bride

Let p be the statement “Life is pain,” D(x) be the proposition “x says that life isn’t pain,” and let S(x,y) be the proposition “x is selling y.” Translate the logical statement

p \land \forall x(D(x) \Rightarrow \exists y S(x,y)).

This matches two of the great lines from The Princess Bride.

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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.

Happy E Day! (British version)

Using the British day/month/year format of abbreviating dates, today is 2/7/18, matching the first four significant digits in the decimal expansion of e.

Using the British convention, it’ll be e Day again on 27/1/82, or January 27, 2082. I doubt I’ll personally be around to see that one, but I was alive to enjoy January 27, 1982. At the time, I was (barely) old enough to know the significance of the number e, but I wasn’t old enough to know that other parts of the world abbreviate dates in a way different than Americans.