Hello World!
There is no doubt that the vacuous truth is a challenging topic for me. Who thinks that all employees who earn over 80 trillion are both tall and short? I guess it's true.
For me, I see the "both tall and short" and totally reject the statement. It's not possible for something to be those at the same time, there is a set of tall people and a set of short people and there is no intersection. The trick is, there are no employees that make 80 trillion. Then, the set of all employees who make over 80 trillion is the empty set. When we talk about "all of the people" in and empty set everything we say about it is true; tall & short, male & female. This idea extends to any implication where the antecedent is considering an empty set. For example, "If a pig flies, then it has wings" is a true statement. The antecedent "flying pigs" is considering an empty set - there are no flying pigs. Since there are no flying pigs we can say anything about them and it will still be true.
This is the essence of the vacuous truth, it's essentially a statement about all of the elements in an empty set - and that statement is always true because the set it empty.
