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De Morgan Laws

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.

Using gates (commonly used in Digital Electronics), they can be expressed in two forms:

the OR form:

the AND form:
DeMorgan's law

In Matlab, these laws can be demonstrated 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 demonstrate the OR form of the law
% with these two lines
x_or_y = x|y
DeMorg1 = not(not(x)& not(y))

% We can demonstrate 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 demonstrates the De Morgan's laws.

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