Verify the second distributive law and the identity and inverse laws for Example 15.25.
Example 15.25
Let B be the set of all positive integer divisors of 30: B = {1, 2, 3, 5, 6, 10, 15, 30}. For all x, y ∈ B, define x + y = lcm(x, y); xy = gcd(x, y); and x = 30/x. Then with 1 as the zero element and 30 as the unity element, one can verify that (B, +, ∙, ¯, 1, 30) is a Boolean algebra.