Please help with this question!!!

Question

Consider the set

          .

Which of the following is the corresponding set builder notation for the above set?

a.) 

b.) 

c.)

d.)

Answer 1

This answer gives us all even integers between 2 and 10. This already tells us that (b) cannot be right since it looks at an interval of real numbers. If you look at (c), it is actually odd numbers {3, 5, 7, ..., 11}, so this does not work. Option (d) is almost right, but it does not include 10 and so it fails. Thus, the only answer is (a), which can readily be seen to be correct because for k = 1 we have x = 2 in the set, for k = 2 we have x = 4 in the set, and so on until k = 5 which gives us x = 10 in the set, producing the overall set of {2, 4, 6, 8, 10}.