Boolean Algebra

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Section 10.1 Boolean Algebra

A Boolean algebra is a bounded lattice that is both complemented and distributive. Let’s define the is_boolean_algebra() function to determine whether a given poset is a Boolean algebra. The function accepts a finite partially ordered set as input and returns a tuple containing a boolean value and a message explaining the result. Run the following cell to define the function and call it in other cells.

Let’s check if the following poset is a Boolean algebra.

When we pass P to the is_boolean_algebra() function, LatticePoset() raises an error because P is not a lattice. The ValueError provides more information about the absence of a top element. Therefore, P is not a Boolean algebra.

Let’s examine the divisor lattice of 30:

Now for the divisor lattice of 20:

Here is a classic example in the field of computer science:

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