Question

Write the set of all positive integers whose cube is odd.

Answer 1

As the cube of an odd integer is odd, and an odd positive integer has the form 2n +1 for some $n\underset{–}{>}0$.

Hence the set of all positive integers whose cube is odd may be written in set builder form as { $xϵZ,x=2n+1,n\underset{–}{>}0$ }.