For questions regarding functionally complete sets of Boolean functions, that is, logical connectives.
Questions tagged [functional-completeness]
6 questions
4
votes
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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) $\{\to,\neg\}$
c) $\{\to\}$
I have looked at the…
user141834
- 143
3
votes
1 answer
How the two derived identities help prove that the 2-basis ensures $\mathtt{NAND}$'s functional completeness?
I am proving that $\mathtt{NAND}$ is functionally complete in Boolean algebra using Robert Veroff’s 2-basis for the Sheffer stroke ($\mathtt{NAND}$) from his paper (A Shortest 2-Basis for Boolean Algebra in Terms of the Sheffer Stroke). I need…
Dang Dang
- 320
3
votes
1 answer
Proof-Theoretic Advantages to Using Only NANDs in Infinitary Logics
This question comes out of a question on Philosophy Stack Exchange, and a particular difference of opinion in regards to the initial question stated in 'Is there any major benefit to using NAND in infinitary logic?'. The question revolves around an…
J D
- 145
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3
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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 functions, F is functionally complete if and only if every binary…
Cantor
- 462
2
votes
2 answers
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 complete). My attempt is that I only have to show that…
Freddy
- 33
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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 classes, there is a member of X which does not…
