# Questions tagged [functional-completeness]

For questions regarding functionally complete sets of Boolean functions, that is, logical connectives.

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### Show that there exists a ternary operator T such that {T} is functionally complete. [closed]

I know that here exists binary operator like that: T(1,1)=0, T(1,0)=1, T(0,1)=1, T(0,0)=1. But how about ternary?
27 views

### Proof Systems, implication of complete and soundness of itself negated

Let $A(S,P,f,g)$ and $B=(S,P,h,i)$ $S$ is the sound set of statements for $A$ and $B$ $P$ is the sound set of proofs for $A$ and $B$ Define $h$ and $i$ as:\begin{align}h(s)=1\iff&\,p(s)=0\\i(s,p)...
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### How does functional completeness relate to expressiveness in higher-order logics?

In first-order logic, the notion of functional completeness is well-defined. But in higher-order logics, where we can quantify over predicates and not just individuals, the notion of functional ...
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### Showing Functional Completeness

I am reading about Functional Completeness in Wikipedia. In the "Formal Definition: "Since every Boolean function of at least one variable can be expressed in terms of binary Boolean ...
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### On the functional-completeness of the Sheffer stroke

I have seen functional-completeness (in regards to boolean functions) defined as: A set X of truth-functions (of 2-valued logic) is functionally complete if and only if for each of the five defined ...
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### proof of functional completeness of logical operators

If I know that the set of operators {∨, & , ¬} is functionally complete, how do I go about proving/disproving the functional completeness of the following set of operators? a) $\{\vee,\neg\}$ b) ...
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### Functional completeness of $\{\text{or},\text{ xor}, \text{ xnor}\}$
I need to prove the functional completeness of $\{\text{or},\text{ xor},\text{ xnor}\}$ with the help of $\{\text{not},\text{ or},\text{ and}\}$ (which have been already proven to be functional ...