Prove NOR is Complete: Logic Problem Solved

  • Thread starter Thread starter zetafunction
  • Start date Start date
  • Tags Tags
    Logic
Click For Summary
NOR is a functionally complete operator, meaning all other logical operations can be expressed using only NOR. To express NOT using NOR, one can use the expression NOT(x) = x NOR x. By applying DeMorgan's laws, AND and OR can be derived as follows: AND(x, y) = NOT(x NOR y) and OR(x, y) = NOT(x) NOR NOT(y). This demonstrates that NOR can replicate the functionality of NOT, AND, and OR, confirming its completeness in logical operations. The discussion emphasizes the ability to construct all basic logical functions solely with the NOR operator.
zetafunction
Messages
371
Reaction score
0
how could i express using only the operator NOR (in logic) the rest of operation NOT(x) AND(x,y) OR(x,y) that is how i could prove that the Logic operator NOR is functionally complete
 
Physics news on Phys.org
See if you can figure out NOT in terms of NOR (this is not too hard), then use DeMorgan's laws to figure out how to write AND and OR using NOT and NOR.
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
View full post »

Similar threads

Undergrad What Are the Axioms of Fuzzy Logic and How Do They Extend Boolean Algebra?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad On the meaning of logical implication within specific context/models
  • · Replies 22 ·
Replies
22
Views
3K
High School Traditional logic and its usefulness in the past
  • · Replies 21 ·
Replies
21
Views
3K
Graduate Prove that points which are indistinguishable from 0 exist (using logic)
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Can you calculate the probability of a complex logic expression?
  • · Replies 3 ·
Replies
3
Views
2K
High School ##A \subset B \iff \exists x \in B \land x \not\in A##?
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad What is truth in the completeness theorem?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Contrapositive of theorem and issue with proof
  • · Replies 5 ·
Replies
5
Views
2K
High School What is the usefulness of formal logic theory?
  • · Replies 1 ·
Replies
1
Views
3K
Can the shunting-yard algorithm handle logic processing?
  • · Replies 2 ·
Replies
2
Views
2K