To find the number of subsets that can be generated from a set containing 8 unique integers with the restriction that there must be an odd number of elements in each subset, we can follow these steps:
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Calculate Total Subsets: The total number of subsets of a set with \( n \) elements is given by \( 2^n \). For our set with 8 unique integers, the total number of subsets is: \[ 2^8 = 256 \]
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Calculate Even and Odd Subsets: Subsets can be classified into those with an even number of elements and those with an odd number of elements. Since the total number of subsets is \( 2^n \), and the subsets can be evenly split into odd and even counts for sets of unique elements, we can conclude that: \[ \text{Number of odd subsets} = \text{Number of even subsets} = \frac{2^n}{2} = \frac{256}{2} = 128 \]
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Conclusion: Therefore, the number of subsets that contain an odd number of elements is: \[ \boxed{128} \]