Question

a television network surveyed 500 families to determine how many families watched the networks tuesday evening shows. the results are shown in the diagram below.
u = set of 500 surveyed
x = set of families who watched show x.
y = set of families who watched show y.
how many families watched both show x and y?
78
204
394
112

Explanation:

Step1: Understand the Venn diagram

In a Venn diagram, the overlapping region represents the elements common to both sets. Here, set \(X\) is families watching show \(X\), set \(Y\) is families watching show \(Y\), and the overlapping part of the two circles in the Venn diagram represents families watching both shows.

Step2: Identify the overlapping value

Looking at the given Venn diagram, the number in the overlapping region of circles \(X\) and \(Y\) is \(78\).

Answer:

78