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Calculation of N(A ∩ (Y ∩ N)'):
First, we need to find out the elements of the sets involved in the equation:
A = set of Adult Males
C = Common set of Women and Youth
Y = set of positive opinion
N = set of negative opinion
Now, we need to find out the complement of (Y ∩ N):
(Y ∩ N)' = Y' ∪ N'
Then, we need to find out the intersection of A and (Y ∩ N)':
A ∩ (Y ∩ N)' = A ∩ (Y' ∪ N')
Since we don't have enough information about the overlap between Y and N, we can't simplify this expression further. But we can use the given data to estimate the sizes of the sets:
- Out of 35 adult males and females, 30 have a negative opinion or are unsure about their voting choice.
- Out of 25 youth over 18 years, 15 have a positive opinion about their voting choice.
So, we can say that:
- Y is a set of at least 15 elements (positive opinions of youth over 18 years).
- N is a set of at least 30 elements (negative opinions or undecided voters among adult males and females).
- C is a set of at least 50 elements (total number of adult males, adult females, and youth over 18 years).
Therefore, we can conclude that:
- A ∩ (Y ∩ N)' is a set of at least 10 elements (number of adult males with a negative opinion or undecided about their voting choice).
In HTML bullet points:
Calculation of N(A ∩ (Y ∩ N)'):
- Find the elements of the sets involved in the equation: A, C, Y, N.
- Find the complement of (Y ∩ N): (Y ∩ N)' = Y' ∪ N'.
- Find the intersection of A and (Y ∩ N)': A ∩ (Y ∩ N)' = A ∩ (Y' ∪ N').
- Use the given data to estimate the sizes of the sets:
- Y is a set of at least 15 elements.
- N is a set of at least 30 elements.
- C is a set of at least 50 elements.
- Therefore, A ∩ (Y ∩ N)' is a set of at least 10 elements.