If 25 days are chosen, then the first 24 may be selected by taking 2 days from each of the 12 months. At this point, the 25th day must be selected from one of the 12 months causing that month to have at least 3 days selected.

With cases means that you need to consider the following cases:

a<=b<=c, a<=c<=b, c<=a<=b, c<=b<=a, b<=a<=c, b<=c<=a

It appears your attempt is one of those cases, now just supply the rest.

You need to come up with rules that will build the given set.

a. {x|x=3n, n is an element of the integers and -1<n<5}

Have fun