114 LOGIC, PART II: THE PREDICATE CALCULUS Chapter 3
- All monotonic functions are one to one. Some monotonic functions are increas-
ing. All increasing functions have inverses. Therefore all monotonic functions have
inverses. - An argument can be valid without the conclusion's being true. If the premise is
true, the argument is valid if and only if the conclusion is true. Hence a sufficient
condition for an argument to be valid is that the premise and conclusion both be
false.