What is an intuitive way to explain and understand De Morgan's Law?

De Morgan's Law is often introduced in an introductory mathematics for computer science course, and I often see it as a way to turn statements from AND to OR by negating terms.

Is there a more intuitive explanation for why this works rather than just remembering truth tables? To me this is like using black magic, what's a better way to explain this so that it makes sense to a less mathematically inclined individual?

Insert real-world predicates and read aloud, for instance:


It can not be both winter and summer (at any point in time).

and


(At any point in time) It is not winter or it is not summer.

Clearly, the two statements are equivalent.

StackExchange Computer Science Q#350, answer score: 14