# elmentary math for educators

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?

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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.

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