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This is not the Cartesian Product

Friday's Saturday Morning Breakfast Cereal lies to you all!

It gives the misleading impression that it is the union of the set of professional titles (A) and the set of acceptable pet names (B) which yields irritating things one can call their spouse. However, I think it is plainly obvious that "Sergeant Cutiepie" is not in A. Therefore, it cannot be that "Sergeant Cutipie" or similar names are in A B. What's going on here is a bit more complex. Define a function cat over A X B such that cat(<a,b>) is the concatenation of a title in A and a pet name in B. The most irritating things one can call one's spouse is the image of A X B under cat.