However, if we represent each divisor of n by the set of its prime factors, we find that this nonconcrete Boolean algebra is to the concrete Boolean algebra consisting of all sets of prime factors of n, with union corresponding to least common multiple, intersection to greatest common divisor, and complement to division into n.
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Again the answer is yes.
This example is an instance of the following notion.
These semantics permit a translation between tautologies of propositional logic and equational theorems of Boolean algebra.
Otherwise, the result is false.