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?
14 (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 \(|A \cup B|\) 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 the intersection of \(A\) 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 \(|A| = 71\), \(|B| = 62\), and \(|A \cap B| = 37\).

Step2: Apply the inclusion - exclusion formula.

Substitute the values into the formula: \(|A \cup B|=|A| + |B|-|A \cap B|\)
\(= 71+62 - 37\)
First, calculate \(71 + 62=133\). Then, calculate \(133-37 = 96\).

Answer:

96