SOLUTION: Suppose B is a proper subset of C. (a)If n(C)5 8, what is the maximum number of elements in B? (b) What is the least possible number of elements in B?

I can't understand  "n(C)5 8".  Did you mean "n(C) = 58"?

The smallest proper subset of any set is the empty or null set .

The largest proper subset of any finite non-empty set is the set
of all but one of its elements (members) but one.

There is only one "improper" subset of any set, and that is the set itself.

So the answer to (b) is 0, and the answer to (a) assuming
you meant "n(C) = 58", is 57.

Edwin