Question

a survey of 112 high school students determined whether they used instagram, twitter, or facebook. the provided information was determined
64 used instagram
60 used twitter
73 used facebook
31 used instagram and twitter
40 used instagram and facebook
39 used twitter and facebook
20 had all three features
complete parts a) through e)

a) how many of the students surveyed used only instagram?
13 (type a whole number.)
b) how many of the students surveyed used instagram and twitter, but not facebook?
11 (type a whole number.)
c) how many of the students surveyed used instagram or twitter?
(type a whole number.)

Explanation:

Step1: Recall the principle of inclusion - exclusion for two sets.

The formula for \(|A \cup B|\) (the number of elements in set \(A\) or set \(B\)) is \(|A|+|B|-|A\cap B|\), where \(|A|\) is the number of elements in set \(A\), \(|B|\) is the number of elements in set \(B\), and \(|A\cap B|\) is the number of elements in both \(A\) and \(B\). Let \(A\) be the set of students who used Instagram and \(B\) be the set of students who used Twitter. We know that \(|A| = 64\), \(|B|=60\), and \(|A\cap B| = 31\).

Step2: Apply the inclusion - exclusion formula.

Substitute the values into the formula: \(|A\cup B|=|A| + |B|-|A\cap B|\). So \(|A\cup B|=64 + 60-31\). First, calculate \(64 + 60=124\), then \(124-31 = 93\).

Answer:

93