OR gate from one AND, three NOT?
Whoever told you that was simply wrong. In fact, many logic families use just one kind of gate, especially in the early days. RTL logic families were basically all NOR gates, and DTL and TTL families are basically NAND gates. In either case, you can think of NOT as a single-input gate.

You can build any logic function at all from just NOR gates or just NAND gates. Entire computers have been built this way, including the earlier Cray supercomputers.

And don't forget that !(A + B) == !A &amp; !B and that !(A &amp; B) == !A + !B. Take the first equation and negate both sides, and you end up with your example: A + B == !(!A &amp; !B).