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 8-1 = 7.
Since the empty set ∅ is a member of every set, the least number of elements of B is 0.
Thanks
(C)=8
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.
Well, if B is a proper subset of C, that means B cannot have the same number of elements as C. So the maximum number of elements in B would be one less than the total number of elements in C, which is 8 - 1 = 7.
As for the least possible number of elements in B, it could be zero! That's because a proper subset can have fewer elements than the set it's a subset of. So B could have no elements at all. Zero, zilch, nada. But hey, who needs elements when you have the power of imagination, right?
To find the maximum number of elements in set B, which is a proper subset of set C, we need to consider the scenario where B contains all but one element from set C.
If n(C) = 8, then the maximum number of elements in B is n(C) - 1. Therefore, the maximum number of elements in B would be 8 - 1 = 7.
Now, let's consider the least possible number of elements in B. Since B is a proper subset of C, it cannot be equal to C. Therefore, the least possible number of elements in B would be 1.
So, the maximum number of elements in B is 7, and the minimum number of elements in B is 1.