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...

Discrete math
asked 2021-01-05
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 \(\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots\)

Answers (1)

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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