Another type of functionally complete operation is a NAND (Not-AND) gate is a binary operation that takes two input values (A and B), and returns false (0) only if A and B are true, otherwise it returns true (1). Truth table of a NAND gate looks like this:

A | B | NAND(A, B)
-|-|-
0 | 0 | 1
1 | 0 | 1
0 | 1 | 1
1 | 1 | 0

Just like NOR gate it can be used to construct any logic gate, eg. NOT, OR, AND. When expressed using NAND gates, these expressions look like this:

- NOT(A) = NAND(A, A)
- OR(A, B) = NAND(NAND(A, A), NAND(B, B))
- AND(A, B) = NOT(NAND(A, B)) = NAND(NAND(A, B), NAND(A, B))

Note that functional completeness refers to sets of logic gates. {NOR} and {NAND} are sets we discussed, but there are other sets, eg. {NOT, AND} and {NOT, OR} that can also derive basic gates. For example {NOT, AND} can be used to derive NAND(A, B) = NOT(AND(A, B)), and as shown above this gate can be used to construct other logic gates.
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