It’s got that swing, if it do mean a thing.

An adapted excerpt of an e-mail:

It has been called to my attention that some of you may have confused the word “contrapositive” with the word “contraceptive” in my e-mail about swing dancing on this coming Saturday. (The party is from 8pm-12am, by the way, with a mini-lesson from 8pm-9pm.) I realize that I used some big words in that e-mail. In order to be above reproach, I will provide the definition of “contrapositive,” although I am really going to look like a nerd by the end of this. Thank you to my friend Dan for drawing this possible confusion to my attention. I also wish to thank Dan for knowing the definition of “contrapositive” and appreciating my witty humor.

The Merriam-Webster Online Dictionary defines “contrapositive” as:

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;

“if not-B then not-A” is the contrapositive of “if A then B”

For example:

Say you have the theorem, “It don’t mean a thing, if it ain’t got that swing.”

We can break this statement into its hypothesis and conclusion.

Its hypothesis, which we will call “A,” is the “if” part: if it ain’t got that swing. Its conclusion, which we will call “B,” is the “then” part: It don’t mean a thing.

I can rearrange the statement into “If A, then B” form, which is as follows:

“If it ain’t got that swing, [then] it don’t mean a thing.”

Now, in order to get its contrapositive, I have to negate both A and B and interchange them, such that the statement is in its “If not-B, then not-A” form.

The negation of A, “If it ain’t got that swing,” is, “If it [has got] that swing,” or, “If it’s got that swing.” Notice that now A has the opposite meaning. This is “not-A.”

Similarly, the negation of B, “It don’t mean a thing,” is, “It do mean a thing.” This is “not-B.”

When I plug these statements back into the formula for a contrapositive (If not-B, then not-A), I get: If it do mean a thing, [then] it’s got that swing.

I then rearranged this sentence into the permutation that followed the original format of, “It don’t mean a thing, if it ain’t got that swing,” which has the “if” part at the end of the sentence.

The result is: It’s got that swing, if it do mean a thing.

This, the contrapositive of, “It don’t mean a thing, if it ain’t got that swing,” was in the subject line of the e-mail I sent.