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. (c) (10 Points) Determine \( n(A \cap C) \).

To determine \( n(A \cap C) \), we need to find the intersection of sets \( A \) and \( C \). The intersection of two sets includes all elements that are common to both sets. ### Step 1: Identify the elements of sets \( A \) and \( C \) - Set \( A = \{a, c, d, e, g, h, m\} \) - Set \( C = \{a, b, e, g, h, k, m\} \) ### Step 2: Find the intersection \( A \cap C \) Now, we will look for elements that are present in both sets \( A \) and \( C \): - From set \( A \): \( a, c, d, e, g, h, m \) - From set \( C \): \( a, b, e, g, h, k, m \) **Common elements:** - \( a \) (in both \( A \) and \( C \)) - \( e \) (in both \( A \) and \( C \)) - \( g \) (in both \( A \) and \( C \)) - \( h \) (in both \( A \) and \( C \)) - \( m \) (in both \( A \) and \( C \)) ### Step 3: List the intersection Thus, the intersection \( A \cap C \) is: \[ A \cap C = \{a, e, g, h, m\} \] ### Step 4: Determine the number of elements in the intersection Now, we count the number of elements in the intersection: \[ n(A \cap C) = 5 \] ### Final Answer Therefore, the number of elements in the intersection \( n(A \cap C) \) is \( 5 \).