Use a Venn Diagram and the given information to determine the number of elements in the indicated set.n(U) = 60, n(A) = 29, n(B) = 17, and n(A ∩ B) = 3. Find n(A ∪ B)'.Group of answer choices
Question
Use a Venn Diagram and the given information to determine the number of elements in the indicated set.n(U) = 60, n(A) = 29, n(B) = 17, and n(A ∩ B) = 3. Find n(A ∪ B)'.Group of answer choices
Solution
To find the number of elements in the set n(A ∪ B)', we first need to find the number of elements in the set n(A ∪ B).
The formula for n(A ∪ B) is n(A) + n(B) - n(A ∩ B).
Substituting the given values into the formula, we get:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 29 + 17 - 3 = 43.
The ' symbol in n(A ∪ B)' denotes the complement of the set, which is the elements not in the set n(A ∪ B).
The formula for the complement of a set is n(U) - n(A ∪ B), where n(U) is the number of elements in the universal set.
Substituting the given values into the formula, we get:
n(A ∪ B)' = n(U) - n(A ∪ B) = 60 - 43 = 17.
So, the number of elements in the set n(A ∪ B)' is 17.
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