Sure. A functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is { AND, NOT }. Each of the singleton sets { NAND } and { NOR } is functionally complete. However, the set { AND, OR } is incomplete, due to its inability to express NOT.

A functionally complete set of gates may utilise or generate 'garbage bits' as part of its computation which are either not part of the input or not part of the output to the system. In a context of propositional logic, functionally complete sets of connectives are also called (expressively) adequate. From the point of view of digital electronics, functional completeness means that every possible logic gate can be realized as a network of gates of the types prescribed by the set. In particular, all logic gates can be assembled from either only binary NAND gates, or only binary NOR gates.

A NOR gate is a logic gate that has two inputs and one output. The output is true if and only if both inputs are false. In other words, the output of a NOR gate is the negation of the AND of its inputs.

A NOR gate is functionally complete because it can be used to create any other logic gate. For example, an AND gate can be created by connecting two NOR gates in series. The output of the first NOR gate will be true if and only if both inputs are false. The output of the second NOR gate will be true if and only if the output of the first NOR gate is false. This is the same as the definition of an AND gate.

Similarly, an OR gate can be created by connecting two NOR gates in parallel. The output of the first NOR gate will be true if and only if both inputs are false. The output of the second NOR gate will be true if and only if either input is true. This is the same as the definition of an OR gate.

Therefore, a NOR gate is functionally complete because it can be used to create any other logic gate.
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