: “Intersection”, is the set of elements of both and
Proof: prove
(where is the set of natural numbers divisible by ) If , then two conditions must be true
To prove the case 1, we have to pick some . We know that and . We can write , where . Because we know that is also divisible by 3, we also know that there must be some such that We got to case 2, where we pick . where Then, (incomplete)