de Morgan's theorems state that
and
The first equation reads "NOT A AND NOT B EQUALS A NOR B" and the second reads "NOT A OR NOT B EQUALS A NAND B"
Proof of these equations by two methods, i.e. by truth tables and by Venn diagrams are available in the Solved Problems at the end of this topic.
The general rules for converting a Boolean expression comprised entirely of ORs(ANDs) to to one consisting entirely of ANDs(ORs) is available in the Lecture 3 summary on Boolean Algebra.