Question

a survey of 120 high school students determined whether they used instagram, twitter, or facebook. the provided information was determined
71 used instagram.
62 used twitter
77 used facebook.
37 used instagram and twitter
46 used instagram and facebook.
38 used twitter and facebook
23 had all three features.
complete parts a) through e).

a) how many of the students surveyed used only instagram?
11 (type a whole number )

b) how many of the students surveyed used instagram and twitter, but not facebook?
(type a whole number )

Explanation:

Step1: Identify the formula for two - set intersection without the third set

To find the number of students who used Instagram and Twitter but not Facebook, we use the formula: \(n(Instagram\cap Twitter\cap \overline{Facebook})=n(Instagram\cap Twitter)-n(Instagram\cap Twitter\cap Facebook)\)

Step2: Substitute the given values

We know that \(n(Instagram\cap Twitter) = 37\) and \(n(Instagram\cap Twitter\cap Facebook)=23\)

So, \(n(Instagram\cap Twitter\cap \overline{Facebook})=37 - 23=14\)

Answer:

14