As reference for others who like me may have been unclear about the term "vacuously true" used in the thread:
(If A then B) is vacuously true if hypothesis A is false.
For example: Let E be the empty set and S any set. Then E is a subset of S:
(If x ϵ E then x ϵ S) is vacuously true because x ϵ E is false. (Reference for others who may also have been un)
Note the last 2 lines in the truth table from post #26 are vacuously true:
* parentheses added to clarify. Pointed out by Deveno.