You can apply a similar equivalence, the contrapositive. Using the same example I gave sidethread:
0. (Premise - I wish to snottily imply that "that guy" did not graduate from high school.)
1. "If that guy graduated from high school, I'm the King of England."
(1) is exactly equivalent to (2):
2. "If I'm not the King of England, that guy didn't graduate from high school."
A positive proposition in (1) is negative in (2), and vice versa. But they are the same thing; if one is defined, the other is also defined.
You can apply a similar equivalence, the contrapositive. Using the same example I gave sidethread:
0. (Premise - I wish to snottily imply that "that guy" did not graduate from high school.)
1. "If that guy graduated from high school, I'm the King of England."
(1) is exactly equivalent to (2):
2. "If I'm not the King of England, that guy didn't graduate from high school."
A positive proposition in (1) is negative in (2), and vice versa. But they are the same thing; if one is defined, the other is also defined.