Question

a survey of 102 college students was taken to determine where they got the news about whats going on in the world. of those surveyed, 31 got the news from news websites, 23 from social media, and 7 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 social media? n(social media only)=16 how many got the news from news websites or social media? n(news websites or social media)=47 how many did not get the news from either news websites or social media? n(neither)=□

Explanation:

Step1: Recall the principle of set - union

The formula for \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), where \(A\) is the set of students who get news from news websites and \(B\) is the set of students who get news from social media. We know \(n(A) = 31\), \(n(B)=23\), and \(n(A\cap B)=7\). And the total number of students surveyed \(N = 102\).

Step2: Calculate the number of students who get news from news websites or social media

Using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), we substitute the values: \(n(A\cup B)=31 + 23-7=47\).

Step3: Calculate the number of students who get news from neither

The number of students who get news from neither news websites nor social media is \(n(\text{Neither})=N - n(A\cup B)\). Substitute \(N = 102\) and \(n(A\cup B)=47\) into the formula. So \(n(\text{Neither})=102 - 47=55\).

Answer:

55