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 the divisor lattice of $30$ is a Boolean algebra.

Now for the divisor lattice of $20\text{:}$

Let’s check if the poset, $P$ is a Boolean algebra.

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

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

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