The difference in the number of elements in the power sets of sets X and Y is 96. The total number of elements in X and Y is _______.
Question
The difference in the number of elements in the power sets of sets X and Y is 96. The total number of elements in X and Y is _______.
Solution
The power set of a set is the set of all possible subsets of the set, including the empty set and the set itself. The number of elements in the power set of a set with n elements is 2^n.
Given that the difference in the number of elements in the power sets of sets X and Y is 96, we can write the equation:
2^|X| - 2^|Y| = 96
However, without additional information, it is not possible to solve this equation for the values of |X| and |Y|. We need more information about the relationship between the sizes of sets X and Y.
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