# MULTIPLE Choice (part 3)

**Discrete Mathematics**Level pending

This is a continuation of MULTIPLE Choice (Part 2).

Why we need to treat empty sets differently? Why only a subset but not a superset gets partial credits? Also, why do we encourage playing safe by only choosing 0 or 1 answer, like what we do in normal "multiple" choice problems?

A problem has 4 answer choices (A, B, C and D). The correct answer is a subset of the set of all answer choices. 2 points are given if your answer is identical to the correct answer, and 1 point is given if your subset is "similar" to the correct subset, that is, there exists exactly one element in the set {A,B,C,D} that is in either your subset or in the correct subset (but not both).

Once again (oh no...) you confront such a problem and have no idea on it. What is your maximal expected value of points if you submit your best attempt?