# Let A_{2}A_{2} be the set of all multiples of 2 except for 2.2. Let A_{3}A_{3} be the set of all multiples of 3 except for 3. And so on, so that A_{n}A_{n} is the set of all multiples of nn except for n,n, for any ngeq2.ngeq2. Describe (in words) the set A_{2} cup A_{3} cup A_{4} cup...

Question
Discrete math
Let $$\displaystyle{A}_{{{2}}}{A}_{{{2}}}$$ be the set of all multiples of 2 except for 2.2. Let $$\displaystyle{A}_{{{3}}}{A}_{{{3}}}$$ be the set of all multiples of 3 except for 3. And so on, so that $$\displaystyle{A}_{{{n}}}{A}_{{{n}}}$$ is the set of all multiples of nn except for n,n, for any $$\displaystyle{n}\geq{2}.{n}\geq{2}$$. Describe (in words) the set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots$$

2021-01-06
Step 1
Let A and B be two sets. Then the union of two sets will be the set that will contain all the elements that are either in set A, either in set B or in both A and B.
Step 2
As set $$\displaystyle{A}_{{{2}}}{A}_{{{2}}}$$ contains all ordered pairs that are multiple of 2 except 2. In the same manner for the other pairs.
Thus, set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup{A}_{{{5}}}\ldots\ldots.$$ will contain all natural numbers except the prime numbers and 1.

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Im confused on this question for Discrete Mathematics.
Let $$\displaystyle{A}_{{{2}}}$$ be the set of all multiples of 2 except for 2. Let $$\displaystyle{A}_{{{3}}}$$ be the set of all multiples of 3 except for 3. And so on, so that $$\displaystyle{A}_{{{n}}}$$ is the set of all multiples of n except for n, for any $$\displaystyle{n}\geq{2}$$. Describe (in words) the set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots$$.
The following problem is solved by using factors and multiples and features the strategies of guessing and checking and making an organized list.
Problem
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