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.

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.