Question

use the venn diagram shown to list the set (a ∩ b ∩ c) in roster form. (a ∩ b ∩ c) = (use a comma to separate answers as needed.)

Explanation:

Step1: Find \( A \cap B \cap C \)

The intersection \( A \cap B \cap C \) is the region common to all three sets \( A \), \( B \), and \( C \). From the Venn diagram, the number in the common region of \( A \), \( B \), and \( C \) is \( 15 \). So \( A \cap B \cap C=\{15\} \).

Step2: Find the complement of \( A \cap B \cap C \)

The complement of a set \( S \) (denoted \( S' \)) consists of all elements in the universal set \( U \) that are not in \( S \). First, we identify all elements in \( U \). The universal set \( U \) includes all numbers in the rectangle: \( 2, 3, 5, 6, 8, 9, 10, 14, 15, 17, 18, 20 \). We exclude the element in \( A \cap B \cap C \) (which is \( 15 \)). So the elements of \( (A \cap B \cap C)' \) are all elements in \( U \) except \( 15 \).

Listing these elements: \( 2, 3, 5, 6, 8, 9, 10, 14, 17, 18, 20 \).

Answer:

\(\{2, 3, 5, 6, 8, 9, 10, 14, 17, 18, 20\}\)