Decide whether or not the set is closed under addition.
{0, 1}
A) Closed B) Not closed
To determine whether or not a set 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, the set is {0, 1}. Let's check all possible combinations of adding two elements together:
0 + 0 = 0, which is in the set.
0 + 1 = 1, which is in the set.
1 + 0 = 1, which is in the set.
1 + 1 = 2, which is not in the set.
Since 2 is not in the set, we can conclude that the set {0, 1} is not closed under addition.
Therefore, the answer is B) Not closed.
To determine whether a set is closed under addition, we need to check if adding any two elements from the set always results in another element within the set.
In this case, we have the set {0, 1}. Let's add all possible pairs of elements from the set and see if the sum is also in the set:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 2
From the calculations, we see that the sum of 0 + 0 = 0 and 1 + 1 = 2 are not in the set. Since there exist pairs of elements whose addition doesn't result in an element within the set, we can conclude that the set {0, 1} is not closed under addition.
Therefore, the answer is B) Not closed.