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 news websites?
n(news websites only)= 24

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)=□

Explanation:

Step1: Recall the principle of set - union

The formula for \(n(A\cup B)\) is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), 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.

Step2: Identify the given values

We know that \(n(A) = 31\) (students from news websites), \(n(B)=23\) (students from social media) and \(n(A\cap B) = 7\) (students from both).

Step3: Calculate \(n(A\cup B)\)

Substitute the values into the formula: \(n(A\cup B)=31 + 23-7\).
\[n(A\cup B)=47\]

Answer:

47