contrapositive (n.): a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them (i.e., “if not-B then not-A” is the contrapositive of “if A then B”)

The contrapositive is an element of formal logic. My knowledge of formal logic is relatively limited, but the basics that, tragically, are not so commonly known go something like this:

Logic is grounded in cause-and-effect statements generally phrased “If A, then B.” These can then be strung together to create more sophisticated chains of deduction like “If A, then B. If B, then C. Therefore, if A, then C.”

The contrapositive is an effect of both negation and reversal. If you have a true statement “If A, then B,” then there are three basic permutations of that statement:

• Negative but not reversed: the inverse: “If not A, then not B.” (false)
• Reversed but not negative: the converse: “If B, then A.” (false)
• Negative and reversed: the contrapositive: “If not B, then not A.” (true)

Of these permutations, only the contrapositive is true. This is an essential fact to know when studying for the LSAT, particularly the Logic Games section, so when I was doing just that a few months ago, the contrapositive was very much on my mind, and so I started thinking about how you could take the contrapositive of certain song lyrics and twist the originals into bizarre shapes that were logically equivalent. Some of the most airtight (and obvious) examples I came up with:

• If I’m not hammering in the morning, then I don’t have a hammer. (Peter, Paul, and Mary, “If I Had A Hammer”)
• If I can’t make it anywhere, I can’t make it there. (Frank Sinatra, “New York, New York”)
• If you’re not taking away the biggest part of me, then you’re not leaving me now. (Chicago, “If You Leave Me Now”)

And some of the wackier ones:

• If it’s useful to sit and wonder why, babe, then you know by now. (Bob Dylan, “Don’t Think Twice It’s Alright”)
• If you don’t call on me and I don’t send it along with love from me to you, then there’s nothing that you want and nothing I can do. (The Beatles, “From Me To You”)
• If it’s not in his kiss, then you don’t want to know if he loves you so. (Betty Everett, “The Shoop Shoop Song (It’s In His Kiss)”)
• If I don’t realize that I love you more than any other guy, then I’m not you. (The Beatles, “No Reply”)