Exercise 1: Translating "Every Function in This Module Has a Docstring" — Possible Solution ==================================================================== CHOOSING THE DOMAIN AND PREDICATES ------------------------------ Domain: all functions (the broad universe of discourse, not just this module's own functions). Two predicates are needed: InModule(x) — "x is a function defined in this module" HasDocstring(x) — "x has a docstring" THE TRANSLATION ------------------------------ for all x, ( InModule(x) -> HasDocstring(x) ) In words: for any function x at all, IF it's in this module, THEN it has a docstring. This matches this chapter's own "every P is a Q" pattern exactly, with P = InModule and Q = HasDocstring. WHY AND (^) WOULD BE THE WRONG CONNECTIVE HERE ------------------------------ Writing "for all x, (InModule(x) ^ HasDocstring(x))" instead would claim that EVERY function in the entire universe of functions - not just this module's own - is simultaneously in this module AND has a docstring. That's a wildly different, and obviously false, statement: it would mean no function exists anywhere outside this one module, since every function would have to satisfy InModule(x). WHY THE -> VERSION IS THE ONLY ONE THAT MATCHES THE ENGLISH MEANING ------------------------------ The original English sentence only makes a claim about functions that happen to be in this module - it says nothing at all about functions elsewhere. The -> version captures exactly that conditional scope: for any function that isn't in this module, InModule(x) is false, and per Chapter 2's own truth table, an implication with a false premise is automatically true regardless of HasDocstring(x) - meaning functions outside the module simply don't affect whether the overall statement holds at all. This is precisely the intended meaning: the claim is only actually "tested" against functions that are in the module. WHY THIS WORKS AS AN ANSWER ------------------------------ It defines an explicit domain and two named predicates, produces the translation using this chapter's own "every P is Q" pattern, and explains concretely why the alternative (^) reading would assert a much stronger and false claim about every function everywhere, not just the ones actually in scope.