Question

let u = {2,4,5,7,8} and a = {4,5,7}. find a. select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\(\bigcirc\\) a. \\(a = \\{\\} \\) (use a comma to separate answers as needed.) \\(\bigcirc\\) b. \\(a = \varnothing\\)

Explanation:

Step1: Recall the definition of complement

The complement of a set \( A \) (denoted \( A' \)) with respect to the universal set \( U \) is the set of all elements in \( U \) that are not in \( A \).

Step2: Identify elements in \( U \) not in \( A \)

Given \( U = \{2, 4, 5, 7, 8\} \) and \( A = \{4, 5, 7\} \). We check each element of \( U \):

• \( 2 \): Not in \( A \), so include in \( A' \).
• \( 4 \): In \( A \), so exclude.
• \( 5 \): In \( A \), so exclude.
• \( 7 \): In \( A \), so exclude.
• \( 8 \): Not in \( A \), so include in \( A' \).

Thus, \( A' = \{2, 8\} \).

Answer:

A. \( A' = \{2, 8\} \)