De Morgan's Laws and Boolean Simplification

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I have a computer science exam soon, and apparently we are supposed to learn De Morgan's Laws as well as Karnaugh Maps for Boolean simplification. However, I can breeze through Karnaugh maps, but I just don't understand what De Morgan's Laws are and how they are used for Boolean simplification.

If anyone could guide me to a helpful web page or explain his laws, it will be much appreciated. Thanks

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DeMorgan's identities, better known as DeMorgan's Theorems, are extremely powerful and heavily used properties of Boolean logic. In essence, they say that and OR gate can be swapped with an AND gate (and vice-versa) without changing the logic function being implemented provided that ALL of the inputs and outputs to the gate are inverted as well.

Read this for proofs and stuff.