Question
Let $S$ be the set of positive divisors of 18 (i.e., $S=\{1,2,3$, $6,9,18\})$. Show that this set together with gcd and $\mathrm{lcm}$ does not form a Boolean algebra.
Step 1
** A Boolean algebra is a set equipped with two binary operations (often denoted as $\wedge$ and $\vee$), a unary operation (often denoted as $\neg$), and two distinguished elements (often denoted as 0 and 1), satisfying certain axioms. These axioms include Show more…
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