Question

use the venn diagram shown to answer the question below.
which regions represent set ( a cup c )?
list the regions that represent the set ( a cup c ).
(type your answer using roman numerals. use a comma to separate answers as needed.)

Explanation:

Step1: Recall Union Definition

The union of sets \( A \) and \( C \) (denoted \( A \cup C \)) includes all elements in \( A \), in \( C \), or in both.

Step2: Identify Regions in A

Set \( A \) includes regions: I (only A), II (A and B), IV (A and C), V (A, B, C).

Step3: Identify Regions in C

Set \( C \) includes regions: IV (A and C), V (A, B, C), VI (B and C), VII (only C).

Step4: Combine Regions for \( A \cup C \)

Combine regions from \( A \) and \( C \), avoiding duplicates: I, II, IV, V, VI, VII.

Answer:

I, II, IV, V, VI, VII