QuestionSurvey 89 students on news sources: 30 use websites, 43 social media, 19 both. Create a Venn diagram and find region sizes.

Studdy Solution

STEP 1

Assumptions1. The total number of students surveyed is89. . The number of students who got the news from news websites is30.
3. The number of students who got the news from social media is43.
4. The number of students who got the news from both news websites and social media is19.

STEP 2

First, we need to find the number of students who only got the news from news websites. We can do this by subtracting the number of students who got the news from both sources from the total number of students who got the news from news websites.
$News\, Websites\, Only = Total\, News\, Websites - Both\, Sources$

STEP 3

Now, plug in the given values for the total number of students who got the news from news websites and the number of students who got the news from both sources.
$News\, Websites\, Only =30 -19$

STEP 4

Calculate the number of students who only got the news from news websites.
$News\, Websites\, Only =30 -19 =11$

STEP 5

Next, we need to find the number of students who only got the news from social media. We can do this by subtracting the number of students who got the news from both sources from the total number of students who got the news from social media.
$Social\, Media\, Only = Total\, Social\, Media - Both\, Sources$

STEP 6

Now, plug in the given values for the total number of students who got the news from social media and the number of students who got the news from both sources.
$Social\, Media\, Only =43 -19$

STEP 7

Calculate the number of students who only got the news from social media.
$Social\, Media\, Only =43 -19 =24$

STEP 8

Lastly, we need to find the number of students who did not get the news from either source. We can do this by subtracting the total number of students who got the news from either source from the total number of students surveyed.
$Neither\, Source = Total\, Surveyed - (News\, Websites\, Only + Social\, Media\, Only + Both\, Sources)$

STEP 9

Now, plug in the given values for the total number of students surveyed, the number of students who only got the news from news websites, the number of students who only got the news from social media, and the number of students who got the news from both sources.
$Neither\, Source =89 - (11 +24 +19)$

STEP 10

Calculate the number of students who did not get the news from either source.
$Neither\, Source =89 - ( +24 +19) =35$ The cardinality for each region of the Venn Diagram is as follows. News Websites Only2. Social Media Only243. Both Sources194. Neither Source35

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