Or, put another way:
When you are performing boolean negation on an expression:
  * Change all ANDs to ORs, and vice-versa
  * Throw a NOT in front of every value
    * (And then, to be clean, change "NOT NOT a" to just "a")

Your original was "(NOT a) OR (NOT b)"
Negating, you get "NOT( (NOT a) OR (NOT b) ) => NOT(NOT a) AND NOT(NOT
b) => a AND b"

If you're still not convinced, sound it out logically:

"DON'T play NFL football IF you're NOT alive OR NOT male"

Is this the opposite?
"DO play NFL football IF you're alive OR male"
No, because that means that alive women may play.

How about this?
"DO play NFL football IF you're alive AND male"
Ah, that's the sexist sport we know and love!