Respuesta :
The number of students who don't take either of these subjects is 34.
Computed using the set theory.
What are the formulas used for set theory?
Assuming two sets A and B, and n(X) represents the cardinal number of the set, that is, the number of elements in the set X, we have formulas:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B),
n(A') = n(U) - n(A)
where A ∪ B is the set of elements that are either in set A or in set B,
A ∩ B is the set of elements that are both in set A and set B, U is the universal set, that is, the set of all elements, and A' is the complement set of A, that is, the set of elements where no element from set A is taken.
How to solve the question?
In the question, we are given that in a group of 60 students, 14 students take Algebra I, 20 students take Algebra II, and 7 students take both subjects.
We are asked to find the number of students who don't take either of the subjects.
To find this, we will use set theory.
The total number of students is in the universal set, U.
Thus, the total number of students in the group can be shown as n(U) = 60.
Assuming Algebra I to be set A, and Algebra II to be set B.
Thus, the number of students taking Algebra I can be shown as n(A) = 14.
The number of students taking Algebra II can be shown as n(B) = 20.
The number of students taking both can be shown as n(A ∩ B) = 7.
Thus, the students taking either Algebra I, or Algebra II, or both can be shown as the set A ∪ B.
The number of elements in the set A ∪ B, can be calculated as:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B),
or, n(A ∪ B) = 14 + 20 - 7 = 26.
Students taking neither can be shown as the set (A ∪ B)'.
The number of students taking neither can be calculated as:
n((A ∪ B)') = n(U) - n(A ∪ B),
or, n((A ∪ B)') = 60 - 26.
Thus, the number of students who don't take either of these subjects is 34. Computed using the set theory.
Learn more about set theory at
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