What is a functionally complete set?

In logic, 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 }, consisting of binary conjunction and negation.Click to see full answer. Keeping this in consideration, why is NAND functionally complete?So, this shows you that NAND gate is functionally complete and any kind of functions, switching expression can be realized using NAND gates alone, because you have already proved you can design a NOT gate, AND gate and OR gate using NAND only. So, continuing with the discussion NOR is also functionally complete.Also Know, how do you prove functionally complete? We can use similar reasoning to prove that any other system of boolean functions is functionally complete. For example, in one of the homeworks, you should have proven that system S = {∧, ¬} is functionally complete. Your proof might have looked as follows: Proof. Secondly, is XOR not functionally complete set of gates? NOR and NAND are the only functionally complete singleton gate sets. Hence, XOR is not functionally complete on its own (or together with NOT, since as point out above NOT can be created using XOR). XOR can be complemented to a two-element functionally complete gate sets.Is decoder functionally complete?decoders are functionally complete..even 2*4 decoders can be used to implement any boolean function..