Solutions
Consider the following least possible Venn diagram,

Conclusions:
I. Some fans are sets → It’s possible but not definite, hence false.
II. Some fans are not set → It’s possible but not definite, hence false.
III. No fan is air → It’s possible but not definite, hence false.
IV. Some air is fans → It’s possible but not definite, hence false.
When we combine the statement III and IV we can say that either III or IV follows.
Hence, either I or II and either III or IV follow.
Additional Information

Important Points
Conditions of Either-or case:
1. The elements should be the same in both statements
2. Individually both the conclusions should be false
3. One conclusion should be positive and one conclusion should be negative (Complementary pair)
The two complementary pairs are:
1) All + Some not
2) No + Some
Mistake Points
1) If two conclusions have the same subject and predicate and consist of a complementary pair but one of the conclusions is true, then it will not form an either-or case.
2) Do not consider “Some + Some” as a complementary pair for the either-or case.
Confusion Points
"Some + Some not" are complementary pairs of Neither nor case.