Let be the proposition “I am running down the road,” let be the proposition “I am trying to loosen my load,” let be the proposition “ is on my mind,” let be the proposition “ is a woman,” let be the proposition “ wants to own me,” let be the proposition “ wants to stone me,” and let be the proposition “ says that is a friend of mine.” Also, let be the index set . Translate the logical statement
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.)
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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