Question: 3. [10pts] An integer is square free if it is the product of distinct primes. For example, 12 is not square free since 12 3-4

3. [10pts] An integer is square free if it is the

3. [10pts] An integer is square free if it is the product of distinct primes. For example, 12 is not square free since 12 3-4 3 22 3.2 2, but 14 is square free since 14 7.2. Recall that Dn is the set of all divisors of n, and notice that (Dn,) is a Boolean Algebra if and only if n is square free. a) If n is square free integer, what are the atoms of Dn b) Determine which of the following are Boolean Algebras, and if a Boolean Algebra, list their atoms. () D2T (i) Ds ii) D210 (iv) D385

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