Let \( U \) be the universal set, where \( U=\{a, b, c, d, e, f, g, h, i, j, k, l, m, n\} \). Let \( A, B \), and \( C \) be subsets of \( U \), where \[ A=\{a, c, d, e, g, h, m\}, B=\{c, e, f, g, h\} \text {, and } C=\{a, b, e, g, h, k, m\} \text {. } \] Do the following, showing all your work and including your name on your slide(s) using the Microsoft PowerPoint application available via the Quick Access menu after logging into my.CCC.edu. Images of handwritten work are not acceptable for this assignment. An editor such as Mathcha (online Math editor), Microsoft PowerPoint Equation Editor, etc., can be used. (d) (10 Points) Determine \( n(B \cap C) \).

To determine \( n(B \cap C) \), we need to find the intersection of sets \( B \) and \( C \), which consists of the elements that are common to both sets. ### Step 1: Identify the elements of sets \( B \) and \( C \) - Set \( B = \{c, e, f, g, h\} \) - Set \( C = \{a, b, e, g, h, k, m\} \) ### Step 2: Find the intersection \( B \cap C \) The intersection \( B \cap C \) includes elements that are present in both \( B \) and \( C \). - From set \( B \), the elements are \( c, e, f, g, h \). - From set \( C \), the elements are \( a, b, e, g, h, k, m \). Now, we will compare the elements of both sets: - \( c \) is not in \( C \). - \( e \) is in both \( B \) and \( C \). - \( f \) is not in \( C \). - \( g \) is in both \( B \) and \( C \). - \( h \) is in both \( B \) and \( C \). ### Step 3: List the common elements The common elements in both sets are: - \( e \) - \( g \) - \( h \) Thus, we have: \[ B \cap C = \{e, g, h\} \] ### Step 4: Determine the number of elements in the intersection The number of elements in the intersection \( n(B \cap C) \) is the count of the elements in the set \( \{e, g, h\} \). \[ n(B \cap C) = 3 \] ### Final Answer Therefore, the final answer is: \[ n(B \cap C) = 3 \]