Nino lays down some logical reasoning in Noel Canning:
Yet the majority contends that “to the extent that the Senate or a Senate committee has expressed a view, that view has favored a functional definition of ‘recess’ [that] encompasses intra-session recesses.” Ante, at 14. It rests that contention entirely on the 1905 Judiciary Committee Report. This distorts what the committee said when it denied Roosevelt’s claim that there had been a recess. If someone avers that a catfish is a cat, and I respond by pointing out that a catfish lives in water and does not have four legs, I have not endorsed the proposition that every land-dwelling quadruped is a cat. Likewise, when the Judiciary Committee explained that an instantaneous transition from one session to another is not a recess because the Senate is never absent, it did not suggest that the Senate’s absence is enough to create a recess. To assume otherwise, as the majority does, is to commit the fallacy of the inverse (otherwise known as denying the antecedent): the incorrect assumption that if P implies Q, then not-P implies not-Q. Contrary to that fallacious assumption, the Judiciary Committee surely believed, consistent with the Executive’s clear position at the time, that “the Recess” was limited to (actual, not constructive) breaks between sessions.
Let me break that down for you:
P –> Q does not imply that ~P –> ~Q