The least possible Venn diagram as per the given statement is as follow:
Conclusions:
I. Some Helmets are Prizes → False (There is no direct relation given between prizes and helmets so it can be possible but not definite, hence, false)
II. Some erasers are pictures → False (There is no direct relation given between erasers and pictures so it can be possible but not definite, hence, false)
III. No helmet is a Prize → False (There is no direct relation given between prizes and helmets so it can be possible but not definite, hence, false)
Thus, Conclusion 1 and 3 will form the complementary pairs for the either-or case.
Hence, the correct answer is "Either conclusion I or III follows".
Additional Information
In this section two of the given conclusion forms a complementary pair for the either-or case.
Complementary pairs for Either or case are:
1) Some + No
2) All + Some not
Rules for Either or Case:-
Rule:
- Subject and Predicate of the element should be the same.
- Two of the conclusions should be can't be determined.
- Both should form a complementary pair.