Please refer to page no. 791 of The Cambridge Grammar of the English Language.
Both in chapter 15 and in this snippet it says or implies that either one or some of the coordinated elements are true. And in light of that, sentence 17(a) should read like that:
Either Kim wasn't at work on Monday or Pat wasn't at work on Tuesday is to be true to make sentence 17(a) true. Right?
If that be the case, then the claim But for [17a] to be true, both of [18i-ii] must be false should not hold. Why both, why not any one of them at minimum based on the logic stated above?