Question

a survey of 100 college students was taken to determine where they got the news about whats going on in the world. of those surveyed, 41 got the news from news websites, 37 from social media, and 22 from both news websites and social media. construct a venn diagram and determine the cardinality for each region. use the completed venn diagram to answer the following questions.
how many got the news from only news websites?
n(news websites only) = \square

Explanation:

Step1: Define the sets

Let \( N \) be the set of students who got news from news websites, and \( S \) be the set from social media. We know \( n(N) = 41 \), \( n(S) = 37 \), and \( n(N \cap S) = 22 \).

Step2: Calculate only news websites

To find the number of students who got news only from news websites, we use the formula for the cardinality of a set difference: \( n(N \text{ only}) = n(N) - n(N \cap S) \).

Substitute the values: \( n(N \text{ only}) = 41 - 22 = 19 \).

Answer:

19