Suppose B is proper subset of C.

Question

If n(c)=8, what is the maximum number of elements n B?

What is the least possible number of elements B?

Answer 1

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 8-1 = 7.

Since the empty set ∅ is a member of every set, the least number of elements of B is 0.

Answer 2

Thanks

Answer 3

(C)=8

Answer 4

I assume you meant to write "C = 8". In this case, the answer would be:

If B is a proper subset of C, the maximum number of elements of B would be 7.

However, we cannot determine the least possible number of elements of B just from the fact that C has 8 elements. It would depend on what other information we have about the relationship between B and C.