Question

a. if n(c) = 8, what is the maximum number of elements in b? b. if n(b) = 8, what is the maximum number of elements in c? ... what is the maximum number of elements that b could have? the maximum number of elements in b is 7. there is no limit on how many elements b could have. b. what is the maximum number of elements in c? a. the maximum number of elements c could have is blank b. there is no limit on how many elements set c could have

Explanation:

Part a: Maximum number of elements in \( B \)

Step 1: Recall subset definition

A proper subset \( B \) of \( C \) means \( B \subseteq C \) and \( B
eq C \). So \( n(B) < n(C) \).
Given \( n(C) = 8 \), the maximum \( n(B) \) is \( 8 - 1 = 7 \).

Step 1: Recall subset relationship

If \( B \) is a proper subset of \( C \), \( C \) must have more elements than \( B \). Given \( n(B) = 8 \), \( C \) can have any number greater than 8, but there's no upper limit (infinite or unbounded in theory for set size unless restricted). But if we consider finite sets, the maximum isn't bounded (or "no limit" as per options).

Answer:

7

Part b: Maximum number of elements in \( C \)