This python code demonstrates distributive law of boolean logic

distributive_boolean.py

# coding: utf-8
from itertools import product


def logic(x, y, z):
    """
    (
        X OR (y AND z) = (x OR y) AND (x OR z)
        AND
        X AND (y OR z) = (x AND y) OR (x AND z)
    )
    """
    a = x or (y and z)
    b = (x or y) and (x or z)

    c = x and (y or z)
    d = (x and y) or (x and z)

    return (a == b) and (c == d)


inputs = list(product([0, 1], repeat=3))
print(*inputs, sep="\n")
"""
>>> (0, 0, 0)
>>> (0, 0, 1)
>>> (0, 1, 0)
>>> (0, 1, 1)
>>> (1, 0, 0)
>>> (1, 0, 1)
>>> (1, 1, 0)
>>> (1, 1, 1)
"""

for xx in inputs:
    if logic(*xx):
        continue
    raise ValueError("not true!")