Home
Welcome
Matrixmania Blog
Sitemap / Search
-> Books <-
Forums and Help
Contact
Basics
Quick Matlab Guide
Matlab Tutorial
Matlab Examples
Matlab Flow Control
Boolean Logic
Plots and GUI
Matlab 2D Plots
Matlab 3D Plots
Matlab GUI
Applications
Calculus
Linear Algebra
Matlab Cookbook I
Matlab Cookbook II
Electrical Calc
Probab and Stats
Finance Apps
Other
Online Calculators
Relevant Links
Notes on Comp
Fun!
Scilab
Your own Website?
Terms/Policies
De Morgan Laws - Boolean logic
In
Boolean Algebra
, there are some very important laws which are called the
De Morgan's laws
(the spelling can change from author to author).
These laws teach us how to interchange NOT with AND or OR logical operators.
In formal logic, De Morgan's laws are rules relating the logical operators 'and' and 'or' in terms of each other via negation:
not(p or q) =
(not p) and (not q)
not(p and q) =
(not p) or (not q)
Using logic gates (commonly used in Digital Electronics), they can be expressed in two forms:
the OR form:
the AND form:
In Matlab, these laws can be confirmed very easily.
Let's create a script file like this:
% Let x and y be column vectors
x = [0 0 1 1]'
y = [0 1 0 1]'
% We can confirm the OR form of the law
with these two lines
x_or_y = x|y
DeMorg1 = not(not(x)& not(y))
% We can verify the AND form of the law
with these two lines
x_and_y = x&y
DeMorg2 = not(not(x) | not(y))
When we run it, we get this output:
x =
0
0
1
1
y =
0
1
0
1
x_or_y =
0
1
1
1
DeMorg1 =
0
1
1
1
x_and_y =
0
0
0
1
DeMorg2 =
0
0
0
1
Which confirms the De Morgan's laws.
From 'De Morgan laws' to home
From 'De Morgan laws' to 'Boolean Algebra' Menu
Top
Boolean Axioms
Logic Operators