Predicate Logic and Popular Culture (Part 42): The Eagles

Let p be the proposition “I am running down the road,” let q be the proposition “I am trying to loosen my load,” let M(x) be the proposition “x is on my mind,” let W(x) be the proposition “x is a woman,” let O(x) be the proposition “x wants to own me,” let S(x) be the proposition “x wants to stone me,” and let F(x) be the proposition “x says that x is a friend of mine.” Also, let I be the index set \{1,2,3,4,5,6,7\}. Translate the logical statement

p \land q \land \exists x_1 \exists x_2 \exists x_3 \exists x_4 \exists x_5 \exists x_6 \exists x_7

(\forall i \in I (M(x_i) \land W(x_i)) \land \forall i \in I ( i \le 4 \Rightarrow O(x_i))

\land \forall i \in I (5 \le i \le 6 \Rightarrow S(x_i)) \land F(x_7)

\forall i \in I \forall j \in I(i \ne j \Rightarrow x_i \ne x_j))

where the domain is all people.

Believe it or not, this forms the opening two lines of the classic song by the Eagles. (The last line of the statement is needed to ensure that the seven women are seven different women.)

green line

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.

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