Question

a survey of 120 high school students asked whether they regularly use instagram and/or facebook. 70 students responded that they use105 students use facebook, and 60 students use both.

a) a= b= c= d=
b) how many students use facebook and not instagram?
c) how many students use facebook or instagram?
d) how many students do not use facebook or instagram?

Explanation:

Step1: Calculate \(A\)

We know that the number of Instagram users is \(70\). Since \(B = 60\) (students who use both), then \(A=\text{Instagram users}-\text{users of both}=70 - 60=10\)

Step2: Calculate \(C\)

We know that the number of Facebook users is \(105\). Since \(B = 60\) (students who use both), then \(C=\text{Facebook users}-\text{users of both}=105 - 60 = 45\)

Step3: Calculate \(D\)

The total number of students is \(120\). The number of students who use Instagram or Facebook is \(A + B+C=10+60 + 45=115\). Then \(D=\text{Total students}-(A + B + C)=120-115 = 5\)

Step4: Answer part b)

Students who use Facebook and not Instagram is \(C = 45\)

Step5: Answer part c)

Students who use Facebook or Instagram is \(A + B + C=10+60+45 = 115\)

Step6: Answer part d)

Students who do not use Facebook or Instagram is \(D = 5\)

Answer:

a) \(A = 10\), \(B = 60\), \(C = 45\), \(D = 5\)
b) \(45\)
c) \(115\)
d) \(5\)