Explain whether the set {0, 1, 2} is closed with respect to addition on whole numbers.

To determine whether the set {0, 1, 2} is closed with respect to addition on whole numbers, we need to check if the sum of any two numbers in the set also belongs to the set.

To get the answer, let's calculate all the possible sums of each pair of numbers in the set {0, 1, 2}:

0 + 0 = 0
0 + 1 = 1
0 + 2 = 2
1 + 0 = 1
1 + 1 = 2
1 + 2 = 3
2 + 0 = 2
2 + 1 = 3
2 + 2 = 4

Looking at these results, we can see that the sums 3 and 4 are not in the set {0, 1, 2}. Therefore, the set {0, 1, 2} is not closed with respect to addition on whole numbers because there are some sums that are not in the set. Specifically, the sums 3 and 4 are missing from the set.