There are two more rules in Boolean Algebra.

 _______   _   _
 (A + B) = A * B

      and
 _______   _   _
 (A * B) = A + B

These give the ability to change between AND and OR family of functions. While the logic is the same, this can help indicate a lot of useful information.

                          ____
      _______        C --|    \
  E = (C * D)            |     )o-- E
                     D --|____/

                          ____
      _   _         C --o\    \
  E = C + D               )    )-- E
                    D --o/____/

In this example of DeMorgan's Theorem, these two gates are logically the exact same, as is the layout. The only difference is that C and D are now free to be manipulated alone. Rather then being "stuck" under the INVERTER function, the parts can now be manipulated individually.

This rule is implemented in schematics a lot when pulse waves are used. If a NAND gate is used in a circuit, it is sometimes represented by an OR gate with inverted inputs when the inputs are normally low and will pulse high. The inverted inputs indicate the normal state of the signal.