Decide whether or not the set is closed under addition.
{0, 1}
A) Closed
B) Not closed
To determine whether the set {0, 1} is closed under addition, we need to check if the sum of any two elements in the set is also in the set.
In this case, we have two elements in the set: 0 and 1. Let's check all possible combinations of adding these elements together.
0 + 0 = 0. Since 0 is also in the set {0, 1}, the sum of 0 and 0 is in the set.
0 + 1 = 1. Again, 1 is in the set {0, 1}, so the sum of 0 and 1 is in the set.
1 + 0 = 1. Once again, the result of adding 1 and 0 is in the set {0, 1}.
1 + 1 = 2. However, 2 is not in the set {0, 1}.
Since 2 is not in the set, one of the sums is not an element of the set, and therefore the set {0, 1} is not closed under addition.
Therefore, the answer is B) Not closed.