Question

A survey of 82 college students was taken to determine where they got the news about​ what's going on in the world. Of those​ surveyed, 34 got the news from​ newspapers, 36 from​ television, and 20 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) =
• How many got the news from only television?
n(Television only) = • How many got the news from newspapers or television?
n(Newspapers or Television) = • How many did not get the news from either newspapers or television?
n(Neither) =

Answer 1

The number of students who got news only from newspapers is 14, only from television is 16, from newspapers or television is 50, and those who did not get news from either source is 32.

Step-by-step explanation:

To construct a Venn diagram and determine the cardinality for each region, we start with the total number of students surveyed, which is 82. According to the survey, 34 got the news from newspapers, 36 from television, and 20 from both newspapers and television.

To find the number of students who got the news only from newspapers, we subtract the number of students who got news from both sources from those who got news from newspapers: 34 - 20 = 14.

To find the number who got the news only from television, we do a similar subtraction: 36 - 20 = 16.

The number who got news from newspapers or television is the sum of those who got news only from newspapers, only from television, and from both: 14 + 16 + 20 = 50.

To find the number who did not get news from either newspapers or television, we subtract the number who got news from at least one of the sources from the total number surveyed: 82 - 50 = 32.

Therefore, n(Newspapers only) = 14, n(Television only) = 16, n(Newspapers or Television) = 50, and n(Neither) = 32.