Respuesta :
Answer:
n(U)=30
n(H)=15
n(G)=18
n(H ∪ G)'=5
n(H ∪ G)=n(U)-n(H ∪ G)'
=30-5=25
So ,n(H ∩ G)=n(H)+n(G)-n(H ∪ G)
=15+18-25=8
Therefore, 8 students take both subjects.
A set is a mathematical model for a collection of diverse things. The total number of students who who take both History and Geography is 8.
What is a set?
A set is a mathematical model for a collection of diverse things; it comprises elements or members, which can be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
Given that there are 30 students in a class. of those, 15 take history, 18 take geography, and 5 take neither of these subjects. Therefore, we can write the following values,
- Total students, n(S)=30
- Students who take History, n(H)=15
- Students who take Geography, n(G)=18
- Students who take neither of the subject, n(H' ∪ G') =5
Now, the number of students who take at least one of the two subject can be written as,
Students who choose at least one subject
= Total students - Students who take neither of the subject
n(H ∪ G) = n(U) - n(H ∪ G)'
n(H ∪ G) = 30 - 5
=25
Further, the total number of students who who take both the subjects can be written as,
Students who take both the subjects = Students who take History + Students who take Geography - Students who choose at least one subject
n(H ∩ G) = n(H) + n(G) - n(H ∪ G)
n(H ∩ G) = 15 + 18 - 25
n(H ∩ G) = 8
Hence, the total number of students who who take both History and Geography is 8.
Learn more about Sets here:
https://brainly.com/question/8053622
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