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DeMorgan's Theorems are:
1. ~(A&B) ~A&~B.
For example:
"It's not raining and cold" means the same as "It is either not raining, or it is not cold", and
"It's not either raining or cold" means the same as "It's not raining and it's not cold".
Applied recursively, DeMorgan's theorem means that to find the inverse of a complex sentence, change all atoms to their inverses, and change all ANDs to ORs and ORs to ANDs.
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