elmentary math for educators
posted by sabrina .
Suppose B is proper subset of C.
If n(c)=8, what is the maximum number of elements n B?
What is the least possible number of elements B?

If B is a proper subset of C, we have
B ⊊ C
This means that B is a any subset of B which is not equal to C. So the maximum number of elements of B is the cardinality of C minus one.
Thus the maximum number of elements of B is 81 = 7.
Since the empty set ∅ is a member of every set, the least number of elements of B is 0.