Decide whether or not the set is closed under addition.
{ 2, 4, 6, 8, . . .}
looks like the set of even whole numbers.
When adding any two even whole numbers, could you ever get a number other than an even whole number ?
NO
To determine whether a set is closed under addition, we need to check if the sum of any two elements in the set is also an element of the set.
The given set is {2, 4, 6, 8, ...}, which represents the set of even numbers starting from 2.
Let's take two arbitrary even numbers from the set: 2 and 6.
The sum of 2 and 6 is 8, which is also an element of the set {2, 4, 6, 8, ...}.
So, in this case, the set is closed under addition because the sum of any two elements in the set is also an element of the set.
Therefore, we can conclude that the set {2, 4, 6, 8, ...} is closed under addition.