Question

use the given venn diagram, which shows the number of elements in regions i through iv to answer the following question. how many elements belong to set a or set b? the number of elements in a or b is \boxed{}.

Explanation:

Step1: Recall the formula for \( n(A \cup B) \)

The number of elements in \( A \) or \( B \) (i.e., \( n(A \cup B) \)) is the sum of the elements in region I, region II, and region III.

Step2: Identify the values in each region

• Region I (only \( A \)): \( 24 \)
• Region II (both \( A \) and \( B \)): \( 22 \)
• Region III (only \( B \)): \( 7 \)

Step3: Calculate the sum

Add the values: \( 24 + 22 + 7 = 53 \)

Answer:

\( 53 \)