Question 26 of 60 (1 point) I Question A Sets \( A, B \), and \( C \) are subsets of the uni These sets are defined as follows. \[ \begin{array}{l} U=\{f, g, h, p, q, r, x, y, z \\ A=\{f, g, p, x\} \\ B=\{g, h, x, y\} \\ C=\{p, r, x, y, z\} \end{array} \] Find \( C \cap(B \cup A)^{\prime} \). Write your answer in roster form or as \[ C \cap(B \cup A)^{\prime}= \] \( \square \)

To solve for \( C \cap (B \cup A)^{\prime} \), we need to follow these steps: 1. Find \( B \cup A \). 2. Determine \( (B \cup A)^{\prime} \). 3. Calculate \( C \cap (B \cup A)^{\prime} \). Let's work through these steps: 1. **Find \( B \cup A \)**: \[ A = \{f, g, p, x\} \] \[ B = \{g, h, x, y\} \] Now take the union: \[ B \cup A = \{f, g, p, x, h, y\} = \{f, g, h, p, x, y\} \] 2. **Determine \( (B \cup A)^{\prime} \)**: The universal set \( U \) is \( \{f, g, h, p, q, r, x, y, z\} \). The complement of \( B \cup A \) in \( U \) is: \[ (B \cup A)^{\prime} = U - (B \cup A) = \{q, r, z\} \] 3. **Calculate \( C \cap (B \cup A)^{\prime} \)**: \[ C = \{p, r, x, y, z\} \] \[ C \cap (B \cup A)^{\prime} = \{p, r, x, y, z\} \cap \{q, r, z\} = \{r, z\} \] Therefore, the answer is: \[ C \cap (B \cup A)^{\prime} = \{r, z\} \]