human
Can you explain why logical NOR is considered a functionally complete operation?
gpt
Yes, logical NOR (also known as negated OR) is considered a functionally complete operation because it can be used to represent all other logical operations, including logical AND, logical OR, and logical NOT.

A functionally complete set of logical connectives is a set of connectives that can be used to represent all other connectives in a logical system. In other words, if you have a functionally complete set of connectives, you can use them to represent any logical statement.

The reason why NOR is functionally complete is because it can be used to create all other logical operations. For example:

NOT A can be represented as A NOR A
A AND B can be represented as (A NOR B) NOR (A NOR B)
A OR B can be represented as (A NOR A) NOR (B NOR B)
This means that if you have a way of computing the NOR operation, you can use it to compute any other logical operation. As a result, NOR is considered a functionally complete operation and is often used as a basis for building more complex logical systems.