Part 1 I have to use symbols in my anwser

Suppose B is proper subset of C
If n(c)=8, what is the maxium number of elements in n (B)
What is the least possible numbers of Elements in B?

Part 2

Suppose C is a subset of D and D is a subset of C
If n (C)=5, find n (D)
What is other relationship exists between sets C and D?

Sabrina has asked these questions before, and the links are:

http://www.jiskha.com/display.cgi?id=1249745879
http://www.jiskha.com/display.cgi?id=1249748610

Part 1:

To find the maximum number of elements in set B, given that B is a proper subset of set C and n(C) is 8, we can deduce that the maximum number of elements in B would be 7.

Explanation:
Since B is a proper subset of C, it means that B contains some, but not all, of the elements of C. Therefore, the maximum number of elements in B would be one less than the number of elements in C. In this case, n(C) is given as 8, so the maximum number of elements in B would be 8 - 1 = 7.

To find the least possible number of elements in B, we need to consider the scenario where B contains the minimum number of elements while still being a proper subset of C. In this case, the minimum number of elements in B would be 1.

Explanation:
A proper subset means that B is a subset of C, but it cannot be equal to C. Therefore, B needs to have at least one element, but not all the elements of C. Therefore, the minimum number of elements in B would be 1.

Part 2:

Given that C is a subset of D and D is a subset of C, the only possibility is that C and D are equal sets.

Explanation:
When one set is a subset of another set, and vice versa, it implies that the sets have the same elements. Therefore, the only relationship that can exist between sets C and D in this scenario is that they are equal sets.

To find the value of n(D) when n(C) is given as 5, we can conclude that n(D) would also be 5 since C and D are equal sets.

Explanation:
If C and D have the same elements, then the number of elements in both sets would be the same. Therefore, if n(C) is given as 5, then the value of n(D) would also be 5, as they are equal sets.