contestada

In a survey, 160 students were selected and asked to write down their favorite subjects in high school. The breakdown of the surveys was as follows: 100 students chose math, 110 students chose biology, 90 students chose chemistry, 65 students chose math and biology, 54 students chose biology and chemistry, 43 students chose math and chemistry, and 20 students chose math, biology, and chemistry. What is the cardinality of the set of students who chose at least one of the three subjects?

Respuesta :

Answer:

The cardinality = 158 students

Step-by-step explanation:

We can find the cardinality of the set of students who chose at least one of the three subjects by using the Venn Diagram formula:

[tex]\boxed{n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)}[/tex]

Let:

  • A = students who chose math
  • B = students who chose biology
  • C = students who chose chemistry

Given:

  • n(A) = 100
  • n(B) = 110
  • n(C) = 90
  • n(A∩B) = 65
  • n(B∩C) = 54
  • n(A∩C) = 43
  • n(A∩B∩C) = 20

[tex]n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)[/tex]

                   [tex]=100+110+90-65-54-43+20[/tex]

                   [tex]=\bf 158\ students[/tex]

Otras preguntas