Question

the venn diagram on the left shows the results of a survey of 60 adults on whether they like apples (a) or oranges (b). find ( a cup b ). type your answer in the boxes

Explanation:

Step1: Recall union formula

The union of two sets \( A \cup B \) is the sum of the number of elements in \( A \) only, \( B \) only, and the intersection.

Step2: Identify regions

• Only Apples (A only): 20
• Intersection (A ∩ B): 10
• Only Oranges (B only): 23
• Also, check the total: 20 + 10 + 23 + 7 = 60 (matches the survey size, so regions are correct).

Step3: Calculate \( A \cup B \)

\( A \cup B = \text{Only A} + \text{Intersection} + \text{Only B} = 20 + 10 + 23 = 53 \). Also, alternatively, total - neither: \( 60 - 7 = 53 \).

Answer:

53