Every day we post a new problem—almost always drawn from the news, though there was a while, back in 2004 (from February 13 to May 23), when we used quotations, proverbs, and sayings instead. To do the problems, you’ll need to have some familiarity with elementary logic.

For each problem, what you need to do is this: (1) specify an appropriate interpretation of the symbols you’re planning to use by (a) identifying a non-empty set of individuals to serve as your universe of discourse (the domain of your interpretation) and (b) associating English expressions of the appropriate type (names or descriptions for constants, n-place predicates for n-place predicates) with the non-logical constants of the notation you intend to use. Then write out in that notation, a formula the truth-conditions are as close as you can make them to the truth-conditions of the sentence you’re trying to translate. Finally, just for fun (well, and for practice too), if your translation isn’t already in prenex normal form, supply an equivalent formula that is.

The particular systems of logic we refer to here and use in our answers are systems presented in the second edition of Benson Mates’s Elementary Logic (New York: Oxford UP, 1972).

The whole idea of this is that practice makes one better and better, if never exactly perfect, and that when it comes to translating things from English into the notation of a system of first-order logic, regular practice, daily practice, is really what’s needed. A week or two on translation problems in a logic course will never make one all that proficient.

Note that we’ve got extensive archives with over ten years’ worth of daily problems, with answers for all the ones that are more than a week old, that you can use to get the hang of how this works and to avail yourself of all sorts of additional opportunities for practice.