For each rational number q, let qZ={qm| m is an element of Z}, so that we have qZ is a subset of Q.

For each rational number q, let qZ={qm| m is an element of Z}, so that we have qZ is a subset of Q.

(a) Use enumeration to describe the sets (1/2)Z, (1/3)Z, (1/2)Z intersects (1/3)Z, (1/2)Z union (1/3)Z, (1/2)Z (1/3)Z, and (3Z)^C (where the compliment is taken inside Z).

(b) What is the smallest natural number n such that every set from part (a) is contained in (1/n)Z?

Z stands for integers and Q stands for rational numbers.

Thanks!