Consider the following family of sets: For any n∈N, we define Q_n={ q \in Q |...

Consider the following family of sets: For any n∈N, we define Q_n={ q \in Q | q= \frac{m} {n^k} for some k, m \in Z}

(That is, Q_n is the set of rational numbers expressed with the denominator that is a power of n.)

a) Is this set closed under addition, subtraction, multiplication, and division?

b) Decide the truth value of the following statement: Q 12 ⊆ Q 18 . Justify.

Expert Solution

Colby Messinger answered 6 months ago

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