TITLE: De Morgan's Second law
QUESTION [5 upvotes]: De Morgan's second law makes sense:  not p and q is the same as not p or not q. However, when I tried to construct a sentence as an example of the law, it seemed not true. For example:
Sequa does not like pie and cake. 
   Sequa does not like pie or does not like cake. 
These sentences appear to not be the same, for the first sentences states that she does not like pie and cake. The second states that she does not like one or the other, not necessarily  that she does not like both. 
Am I giving a incorrect example?

REPLY [2 votes]: (Revised) Your example is correct. Perhaps you are thinking that the second sentence should be: Sequa does not like pie, AND does not like cake? That would be the case if your first sentence had been: Sequa does not like pie OR cake.