Question

a survey of 105 college students was taken to determine where they got the news about whats going on in the world. of those surveyed, 47 got the news from newspapers, 52 from television, and 9 from both newspapers and television. 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 newspapers? n(newspapers only) = □

Explanation:

Step1: Recall Venn - diagram principle

Let \(N\) be the set of students who get news from newspapers and \(T\) be the set of students who get news from television. We know \(n(N\cup T)=105\), \(n(N) = 47\), \(n(T)=52\) and \(n(N\cap T)=9\).

Step2: Use the formula for \(n(N\text{ only})\)

The number of students who get news from only newspapers \(n(N\text{ only})=n(N)-n(N\cap T)\).

Step3: Substitute the values

Substitute \(n(N) = 47\) and \(n(N\cap T)=9\) into the formula: \(n(N\text{ only})=47 - 9\).

Step4: Calculate the result

\(47-9 = 38\).

Answer:

38